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Search: id:A046174
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| A046174 |
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Indices of pentagonal numbers which are also triangular. |
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+0
3
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| 0, 1, 12, 165, 2296, 31977, 445380, 6203341, 86401392, 1203416145, 16761424636, 233456528757, 3251629977960, 45289363162681, 630799454299572, 8785902997031325, 122371842504138976, 1704419892060914337
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = 14*a(n-1) - a(n-2) - 2; g.f.: (1-3*x)/((1-x)*(1-14*x+x^2)) - Warut Roonguthai (warut822(AT)yahoo.com) Jan 05 2001
a(n+1)=7*a(n)-1+2*(12*a(n)^2-4*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 19 2007
a(n)=(1/6)-(1/12)*sqrt(3)*{[7-4*sqrt(3)]^n-[7+4*sqrt(3)]^n}-(1/12)*{[7+4*sqrt(3)]^n+[7-4*sqrt(3)]^n }, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 25 2008]
a(n+1)=15*a(n)-15*a(n-1)+ a(n-2) a(1)=1,a(2)=12,a(3)=165 [From Sture Sjoestedt (sture.sjostedt(AT)spray.se), May 29 2009]
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CROSSREFS
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Cf. A014979, A046175.
Cf. A046175 A014979 A001834.
Sequence in context: A024221 A093152 A143583 this_sequence A055760 A056591 A099745
Adjacent sequences: A046171 A046172 A046173 this_sequence A046175 A046176 A046177
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KEYWORD
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nonn,easy
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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