A046174 Indices of pentagonal numbers which are also triangular.

0, 1, 12, 165, 2296, 31977, 445380, 6203341, 86401392, 1203416145, 16761424636, 233456528757, 3251629977960, 45289363162681, 630799454299572, 8785902997031325, 122371842504138976, 1704419892060914337

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

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

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

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

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

Formula

a(n) = 14*a(n-1) - a(n-2) - 2; g.f.: x*(1-3*x)/((1-x)*(1-14*x+x^2)). - Warut Roonguthai, Jan 05 2001

a(n+1) = 7*a(n) - 1 + 2*sqrt(12*a(n)^2 - 4*a(n) + 1). - Richard Choulet, Sep 19 2007

a(n+1) = 15*a(n) - 15*a(n-1) + a(n-2), a(1)=1, a(2)=12, a(3)=165. - Sture Sjöstedt, May 29 2009

Mathematica

LinearRecurrence[{15, -15, 1}, {0, 1, 12}, 20] (* Harvey P. Dale, Aug 22 2011 *)

Prog

(Magma) [ n eq 1 select 0 else n eq 2 select 1 else 14*Self(n-1)-Self(n-2)-2: n in [1..20] ]; // Vincenzo Librandi, Aug 23 2011

Crossrefs

Cf. A014979, A046175, A001834.

Sequence in context: A231541 A203372 A193104 * A055760 A056591 A331497

Adjacent sequences: A046171 A046172 A046173 * A046175 A046176 A046177

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved