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A093500 (15*n^2 + 5*n + 2)/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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

FORMULA

a(n)= (n+1)*(5*(n+1)^2-5*(n+1)+2)-n*(5*n^2-5*n+2)/2.

Apparently o.g.f = { t/(1-t) + 10 [t/(1-t)]^2 + 15 [t/(1-t)]^3 } / t with a(0) = 1. - Tom Copeland, Oct 11 2008

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(11+3*x+x^2)/(1-x)^3. - Colin Barker, Apr 30 2012

EXAMPLE

a(1) = 11 because (1+1)*(5*(1+1)^2-5*(1+1)+2)-1*(5*1^2-5*1+2)/2 = 2*(5*2^2-5*2+2)-1*(5-5+2)/2 = 2*(20-10+2)/2-1 = 12-1 = 11.

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A044088 A044469 A015246 * A081438 A160483 A034309

Adjacent sequences:  A093497 A093498 A093499 * A093501 A093502 A093503

KEYWORD

easy,nonn

AUTHOR

Michael Joseph Halm, May 13 2004

EXTENSIONS

New definition from Ralf Stephan, Dec 01 2004

Name corrected by Arkadiusz Wesolowski, Aug 15 2011

STATUS

approved

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Last modified March 30 20:18 EDT 2017. Contains 284302 sequences.