A100159 Structured disdyakis triacontahedral numbers (vertex structure 7).

1, 62, 297, 820, 1745, 3186, 5257, 8072, 11745, 16390, 22121, 29052, 37297, 46970, 58185, 71056, 85697, 102222, 120745, 141380, 164241, 189442, 217097, 247320, 280225, 315926, 354537, 396172, 440945, 488970, 540361, 595232

Offset: 1

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

• nonn
• easy

Comments

Also structured deltoidal hexacontahedral numbers (vertex structure 7) (cf. A100158, A100166 = alternate vertices).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100158, A100160 = alternate vertices; A100145 for more on structured polyhedral numbers.

Programs

Magma

[(1/6)*(114*n^3-162*n^2+54*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Formula

a(n) = (1/6)*(114*n^3 - 162*n^2 + 54*n) = n*(19*n^2 - 27*n + 9).

G.f.: x*(1 + 58*x + 55*x^2)/(1-x)^4. [Colin Barker, Apr 16 2012]