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Search: id:A133161
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| A133161 |
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Indices of the triangular numbers which are also centered triangular number. |
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+0
1
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| 1, 4, 16, 61, 229, 856, 3196, 11929, 44521, 166156, 620104, 2314261, 8636941, 32233504, 120297076, 448954801, 1675522129, 6253133716, 23337012736, 87094917229, 325042656181, 1213075707496, 4527260173804, 16895964987721
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n+2)=4*a(n+1)-a(n)+1, a(n+1)=2*a(n)+0.5+0.5*(12*a(n)^2+12*a(n)-15)^0.5.
G.f.: x*(1-x+x^2)/(1-x)/(1-4*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2007
a(n)=-(1/2)-(1/4)*sqrt(3)*[2-sqrt(3)]^n+(1/4)*sqrt(3)*[2+sqrt(3)]^n+(3/4)*[2-sqrt(3)]^n+(3/4) *[2+sqrt(3)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 30 2008
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CROSSREFS
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Cf. A001834 A102871 A128862.
Sequence in context: A051043 A123620 A126929 this_sequence A103820 A084859 A081666
Adjacent sequences: A133158 A133159 A133160 this_sequence A133162 A133163 A133164
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KEYWORD
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nonn,easy
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AUTHOR
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Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 09 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2007
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