NOTATIONS USED 1 NOTATIONS ⎡ (n −1)(m − 2)⎤ Tm,n = n 1+ - Gonal number of rank n with sides m . ⎣⎢ 2 ⎦⎥ n(n +1) T = - Triangular number of rank n . n 2 1 Pen = (3n2 − n) - Pentagonal number of rank n . n 2 2 Hexn = 2n − n - Hexagonal number of rank n . 1 Hep = (5n2 − 3n) - Heptagonal number of rank n . n 2 2 Octn = 3n − 2n - Octagonal number of rank n . 1 Nan = (7n2 − 5n) - Nanogonal number of rank n . n 2 2 Decn = 4n − 3n - Decagonal number of rank n . 1 HD = (9n 2 − 7n) - Hendecagonal number of rank n . n 2 1 2 DDn = (10n − 8n) - Dodecagonal number of rank n . 2 1 TD = (11n2 − 9n) - Tridecagonal number of rank n . n 2 1 TED = (12n 2 −10n) - Tetra decagonal number of rank n . n 2 1 PD = (13n2 −11n) - Pentadecagonal number of rank n . n 2 1 HXD = (14n2 −12n) - Hexadecagonal number of rank n . n 2 1 HPD = (15n2 −13n) - Heptadecagonal number of rank n . n 2 NOTATIONS USED 2 1 OD = (16n 2 −14n) - Octadecagonal number of rank n . n 2 1 ND = (17n 2 −15n) - Nonadecagonal number of rank n . n 2 1 IC = (18n 2 −16n) - Icosagonal number of rank n . n 2 1 ICH = (19n2 −17n) - Icosihenagonal number of rank n . n 2 1 ID = (20n 2 −18n) - Icosidigonal number of rank n . n 2 1 IT = (21n2 −19n) - Icositriogonal number of rank n . n 2 1 ICT = (22n2 − 20n) - Icositetragonal number of rank n . n 2 1 IP = (23n 2 − 21n) - Icosipentagonal number of rank n . n 2 1 IH = (24n 2 − 22n) - Icosihexagonal number of rank n . n 2 1 IHP = (25n2 − 23n) - Icosiheptagonal number of rank n . n 2 1 IO = (26n2 − 24n) - Icosioctagonal number of rank n . n 2 1 IN = (27n2 − 25n) - Icosinonagonal number of rank n . n 2 1 TC = (28n 2 − 26n) - Triacontagonal number of rank n . n 2 2 Obln = n + n - Oblong number of rank n . NOTATIONS USED 3 1 SP = n(n +1)(2n +1) - Square pyramidal number of rank n . n 6 1 PP = n2 (n +1) - Pentagonal pyramidal number of rank n . n 2 1 HXP = n(n +1)(4n −1) - Hexagonal pyramidal number of rank n . n 6 1 HPP = n(n +1)(5n − 2) - Heptagonal pyramidal number of rank n . n 6 1 HP = n(n +1)(5n − 2) - Heptagonal pyramidal number of rank n . n 6 1 TH = n(n +1)(n + 2) - Tetrahedral number of rank n . n 6 1 J = (2n − (−1) n ) - Jacobsthal number of rank n . n 3 n n jn = 2 + (−1) - Jacobsthal Lucas number of rank n . 2 2 CSn = n + (n −1) - Centered square number of rank n . 2 CCn = (2n −1)(n − n +1) - Centered cube number of rank n . 2 CH n = 3n − 3n +1 - Centered Hexagonal number of rank n . 1 CP = (5n2 + 5n + 2) - Centered pentagonal number of rank n . n 2 1 CT = (3n2 − 3n + 2) - Centered Triangular number of rank n . n 2 Gnon = 2n −1 - Gnomonic number of rank n . 4 3 2 Nexn =5n +10n +10n + 5n +1 - Nexus number of rank n . 1 OH = n(2n 2 +1) - Octahedral number of rank n . n 3 NOTATIONS USED 4 Pr on = n(n +1) - Pronic number of rank n . 2 RDn = (2n −1)(2n − 2n +1) - Rhombic dodecagonal number of rank n . 2 SOn = n(2n −1) - Stella octangula number of rank n . 3 2 TOn = 16n − 33n + 24n − 6 - Truncated octahedral number of rank n . 1 TT = (23n2 − 27n +10) - Truncated tetrahedral number of rank n . n 6 Sn = 6n(n −1) +1 - Star number of rank n . 2n n+1 Kn = 2 + 2 −1 - Kynea number of rank n . 1 HO = [(2n −1)(2n2 − 2n + 3)] - Hauy Octahedral number of rank n . n 3 1 PT = n(n +1)(n + 2)(n + 3) - Pentatope number of rank n . n 24 .