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A046175 Indices of triangular numbers which are also pentagonal. 9
0, 1, 20, 285, 3976, 55385, 771420, 10744501, 149651600, 2084377905, 29031639076, 404358569165, 5631988329240, 78443478040201, 1092576704233580, 15217630381229925, 211954248632985376, 2952141850480565345, 41118031658094929460, 572700301362848447101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Colin Barker, Table of n, a(n) for n = 0..874

W. Sierpiński, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liege 33 (1964) 513-517

Eric Weisstein's World of Mathematics, Pentagonal Triangular Number, MathWorld

Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

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, Jan 05 2001

a(n+1) = 7*a(n) + 3 + 2*(12*a(n)^2 + 12*a(n) + 1)^0.5. - Richard Choulet, 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. - Paolo P. Lava, 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 Sjöstedt, May 29 2009

PROG

(PARI) concat(0, Vec(-x*(5*x+1)/((x-1)*(x^2-14*x+1)) + O(x^50))) \\ Colin Barker, Jun 23 2015

CROSSREFS

Cf. A014979, A046174, A001834.

Sequence in context: A017953 A016317 A021404 * A231105 A016314 A021164

Adjacent sequences:  A046172 A046173 A046174 * A046176 A046177 A046178

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)