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