A093500 a(n) = (15*n^2 + 5*n + 2)/2.

11, 36, 76, 131, 201, 286, 386, 501, 631, 776, 936, 1111, 1301, 1506, 1726, 1961, 2211, 2476, 2756, 3051, 3361, 3686, 4026, 4381, 4751, 5136, 5536, 5951, 6381, 6826, 7286, 7761, 8251, 8756, 9276, 9811, 10361, 10926, 11506, 12101, 12711, 13336, 13976, 14631, 15301

Offset: 1

Author

Michael Joseph Halm, May 13 2004

Keywords

• easy
• nonn

Comments

Icosahedral gnomic numbers: first differences of icosahedral numbers.

The sequence is related to other gnomons of polyhedra, known by other more familiar names: triangular (tetrahedral gnomic), hex (cubic gnomic), square pyramidal numbers (octahedral gnomic).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A000330, A003215, A005901, A006564.

Programs

Magma

[(15*n^2+5*n+2)/2: n in [1..50]]; // Vincenzo Librandi, Aug 16 2011

Mathematica

Table[(15n^2+5n+2)/2,{n,50}] (* Harvey P. Dale, Jun 28 2014 *)

PARI

a(n)=(15*n^2+5*n+2)/2 \\ Charles R Greathouse IV, Jun 16 2017

Formula

From Colin Barker, Apr 30 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: (6*x^2 + 8*x + 1)/(1-x)^3. (End)

E.g.f.: exp(x)*(1 + 10*x + 15*x^2/2). - Elmo R. Oliveira, Oct 21 2024

Extensions

New definition from Ralf Stephan, Dec 01 2004

Name corrected by Arkadiusz Wesolowski, Aug 15 2011