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Search: id:A014979
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| A014979 |
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Numbers that are both triangular and pentagonal. |
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+0
3
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| 0, 1, 210, 40755, 7906276, 1533776805, 297544793910, 57722156241751, 11197800766105800, 2172315626468283465, 421418033734080886426, 81752926228785223683195, 15859646270350599313653420
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 22.
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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) = 194a(n-1) - a(n-2) + 16; g.f.: (1+15*x)/((1-x)*(1-194*x+x^2)).
a(n)=((((1+sqrt(3))^(4n-1)-(1-sqrt(3))^(4n-1))/(2^(2n+1)*sqrt(3)))^2)/2-1/8. - John Sillcox (johnsillcox(AT)hotmail.com), Sep 01 2003
a(n)=A076139(2n+1). - Michael Somos, May 30 2005
a(n+1)=97*a(n)+8+7*(192*a(n)^2+32*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 19 2007
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EXAMPLE
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a(2)=40755 which is 285(285-1)/2 = 165(3*165-1)/2.
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PROGRAM
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(PARI) a(n)=subst((-8+15*poltchebi(2*n+1)-poltchebi(2*n))/96, x, 7) - Michael Somos, May 30 2005
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CROSSREFS
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Cf. A046174, A046175.
Sequence in context: A140904 A092711 A089514 this_sequence A134236 A136350 A068297
Adjacent sequences: A014976 A014977 A014978 this_sequence A014980 A014981 A014982
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KEYWORD
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nonn,easy
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AUTHOR
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Glenn Johnston (glennj(AT)sonic.net)
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EXTENSIONS
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Corrected and extended by Warut Roonguthai (warut822(AT)yahoo.com)
Edited by njas, Jul 24 2006
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