A133272 Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).

1, 7, 78, 924, 11005, 131131, 1562562, 18619608, 221872729, 2643853135, 31504364886, 375408525492, 4473397941013, 53305366766659, 635191003258890, 7568986672340016, 90192649064821297, 1074742802105515543

Offset

1,2

Comments

Numbers X such that 140*X^2-140*X+49 is a square.

Also positive integers x in the solutions to 5*x^2 - 7*y^2 - 5*x + 7*y = 0, the corresponding values of y being A253621. - Colin Barker, Jan 06 2015

Also indices of centered pentagonal numbers (A005891) which are also centered heptagonal numbers (A069099). - Colin Barker, Jan 06 2015

Links

Colin Barker, Table of n, a(n) for n = 1..930

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

Formula

a(n+2) = 12*a(n+1)-a(n)-5.

a(n+1) = 6*a(n)-2.5+0.5*(140*a(n)^2-140*a(n)+49)^0.5.

G.f.: x*(-1+6*x)/(-1+x)/(1-12*x+x^2). - R. J. Mathar, Nov 14 2007

a(n) = (1/2)+(1/4)*[6-sqrt(35)]^(n-1)+(1/20)*sqrt(35)*[6+sqrt(35)]^(n-1)+(1/4)*[6+sqrt(35)]^(n-1)-(1/20)*[6 -sqrt(35)]^(n-1)*sqrt(35), with n>=1 - Paolo P. Lava, Jul 14 2008

a(n) = 13*a(n-1)-13*a(n-2)+a(n-3). - Colin Barker, Jan 06 2015

Prog

(PARI) Vec(x*(6*x-1)/((x-1)*(x^2-12*x+1)) + O(x^100)) \\ Colin Barker, Jan 06 2015

Crossrefs

Cf. A000566, A069099, A128919, A253621, A253622.

Sequence in context: A045485 A068621 A210406 * A186657 A079590 A202755

Adjacent sequences: A133269 A133270 A133271 * A133273 A133274 A133275

Keyword

nonn,easy

Author

Richard Choulet, Oct 16 2007

Extensions

More terms from Paolo P. Lava, Jul 14 2008

Status

approved