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Search: id:A046173
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| A046173 |
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Indices of square numbers which are also pentagonal. |
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+0
5
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| 1, 99, 9701, 950599, 93149001, 9127651499, 894416697901, 87643708742799, 8588189040096401, 841554882220704499, 82463790268588944501, 8080609891439495856599, 791817305570802005002201
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
L. Euler, De solutione problematum diophanteorum per numeros integros, par. 21
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FORMULA
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a(n) = 98*a(n-1) - a(n-2); g.f.: (1+x)/(1-98*x+x^2) - Warut Roonguthai (warut822(AT)yahoo.com) Jan 05 2001
a(1-n)=-a(n). - Michael Somos Sep 05 2006
Define f[x,s] = s x + Sqrt[(s^2-1)x^2+1]; f[0,s]=0. a(n) = f[f[a(n-1),5],5]. - Marcos Carreira, Dec 27 2006
a(n)=((12+5*sqrt(6))/24)*(5+2*sqrt(6))^(2*n)+((12-5*sqrt(6))/24)*(5-2*sqrt(6))^(2*n) for n>=0 [From Richard Choulet (richardchoulet(AT)yahoo.fr), Apr 29 2009]
a(n+1)=49*a(n)+10*sqrt(24*a(n)^2+1) for n>=0 with a(0)=1 [From Richard Choulet (richardchoulet(AT)yahoo.fr), Apr 29 2009]
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PROGRAM
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(PARI) {a(n)=subst(poltchebi(n)-poltchebi(n-1), 'x, 49)/48} /* Michael Somos Sep 05 2006 */
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CROSSREFS
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Cf. A036353, A046172.
Sequence in context: A069363 A163051 A093233 this_sequence A098609 A132607 A093211
Adjacent sequences: A046170 A046171 A046172 this_sequence A046174 A046175 A046176
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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