A046175 Indices of triangular numbers which are also pentagonal.

0, 1, 20, 285, 3976, 55385, 771420, 10744501, 149651600, 2084377905, 29031639076, 404358569165, 5631988329240, 78443478040201, 1092576704233580, 15217630381229925, 211954248632985376, 2952141850480565345, 41118031658094929460, 572700301362848447101

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

From Warut Roonguthai, Jan 05 2001: (Start)

a(n) = 14*a(n-1) - a(n-2) + 6.

G.f.: x*(1+5*x)/((1-x)*(1-14*x+x^2)). (End)

a(n+1) = 7*a(n) + 3 + 2*sqrt(12*a(n)^2 + 12*a(n) + 1). - Richard Choulet, Sep 19 2007

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

Mathematica

LinearRecurrence[{15, -15, 1}, {0, 1, 20}, 20] (* Harvey P. Dale, Sep 10 2021 *)

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