A137694 Numbers k such that 6k^2-2k = 3n^2-n for some integer n>0.

5, 5577, 6435661, 7426747025, 8570459630997, 9890302987423321, 11413401077026881245, 13171054952586033533217, 15199386001883205670450981, 17540078275118266757666898665, 20241235130100477955141930608237, 23358367800057676441967030255006641

Offset: 1

Author

M. F. Hasler, Feb 08 2008

Keywords

• easy
• nonn

Comments

Also indices of pentagonal numbers which are half of some other pentagonal number: see A137693 for more details, comments and links.

Links

• Colin Barker, Table of n, a(n) for n = 1..250
• Dario Alpern, Quadratic two integer variable equation solver
• Index entries for linear recurrences with constant coefficients, signature (1155,-1155,1).

Crossrefs

Cf. A000326, A136112-A136118, A135768-A135769, A137693.

Programs

PARI

vector(20,i, (v=if(i>1,[577,408;816,577]*v-[164;232], [5;7]))[1,1])

Formula

a(n) = f^{2n-2}(5,7)[1], where f(x,y) = (577x + 408y - 164, 816x + 577y - 232).

a(n) = (5,7,1,5,7,1,...) (mod 10).

G.f.: -x*(5-198*x+x^2) / ( (x-1)*(x^2-1154*x+1) ). - R. J. Mathar, Apr 17 2011