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Search: id:A093500
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| A093500 |
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(1/2) (15n^2 + 35n + 22). |
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+0
2
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| 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
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OFFSET
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1,1
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COMMENT
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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 (octohedral gnomic)
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FORMULA
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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. [From Tom Copeland (tcjpn(AT)msn.com), Oct 11 2008]
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EXAMPLE
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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
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CROSSREFS
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Cf. A000217, A000330, A003215, A005901, A006564.
Sequence in context: A044088 A044469 A015246 this_sequence A081438 A160483 A034309
Adjacent sequences: A093497 A093498 A093499 this_sequence A093501 A093502 A093503
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KEYWORD
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easy,nonn
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AUTHOR
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Michael Joseph Halm (hierogamous(AT)lycos.com), May 13 2004
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EXTENSIONS
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New definition from Ralf Stephan, Dec 01, 2004
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