A133271 Indices of 7-gonal numbers which are also centered 7-gonal numbers.

1, 8, 92, 1093, 13021, 155156, 1848848, 22031017, 262523353, 3128249216, 37276467236, 444189357613, 5292995824117, 63071760531788, 751568130557336, 8955745806156241, 106717381543317553, 1271652832713654392

Offset: 1

Author

Richard Choulet, Oct 16 2007

Keywords

• nonn

Comments

Numbers X such that 140*X^2-84*X-7 is a square.

Links

• Index entries for linear recurrences with constant coefficients, signature (13, -13, 1).

Crossrefs

Cf. A128919.

Programs

Mathematica

LinearRecurrence[{13,-13,1},{1,8,92},30] (* Harvey P. Dale, Mar 24 2013 *)

Formula

a(n+2)=12*a(n+1)-a(n)-3 ; a(n+1)=6*a(n)-1.5+0.5*(140*a(n)^2-84*a(n)-7)^0.5

G.f.: -x*(1-5*x+x^2)/(-1+x)/(1-12*x+x^2). - R. J. Mathar, Nov 14 2007

a(1)=1, a(2)=8, a(3)=92, a(n)=13*a(n-1)-13*a(n-2)+a(n-3). - Harvey P. Dale, Mar 24 2013

Extensions

More terms from Paolo P. Lava, Jul 08 2008