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A046175
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Indices of triangular numbers which are also pentagonal.
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6
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0, 1, 20, 285, 3976, 55385, 771420, 10744501, 149651600, 2084377905, 29031639076, 404358569165, 5631988329240, 78443478040201, 1092576704233580, 15217630381229925, 211954248632985376, 2952141850480565345
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| W. Sierpinski, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liege 33 (1964) 513-517
Eric Weisstein's World of Mathematics, Pentagonal Triangular Number, MathWorld
Index to sequences with linear recurrences with constant coefficients, signature (15,-15,1).
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FORMULA
| a(n) = 14*a(n-1) - a(n-2) + 6; g.f.: x*(1+5*x)/((1-x)*(1-14*x+x^2)) - Warut Roonguthai (warut822(AT)yahoo.com) Jan 05 2001
a(n+1)=7*a(n)+3+2*(12*a(n)^2+12*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 19 2007
a(n)=-(1/2)+(1/12)*sqrt(3)*{[7-4*sqrt(3)]^n-[7+4*sqrt(3)]^n}+(1/4)*{[7+4*sqrt(3)]^n+[7-4*sqrt(3)]^n }, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 25 2008]
a(n+1)=15*a(n)-15*a(n-1)+ a(n-2) with a(1)=1, a(2)=20, a(3)=285. - Sture Sjostedt (sture.sjostedt(AT)spray.se), May 29 2009
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CROSSREFS
| Cf. A014979, A046174, A001834.
Sequence in context: A017953 A016317 A021404 * A016314 A021164 A017918
Adjacent sequences: A046172 A046173 A046174 * A046176 A046177 A046178
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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