A251927 Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to a heptagonal number H(m) for some m.

0, 8, 76, 1518, 12986, 111034, 2190396, 18727244, 160112392, 3158550954, 27004674302, 230881959670, 4554628286712, 38940721617680, 332931625733188, 6567770830889190, 56152493568021698, 480087173425298866, 9470720983513926708, 80971856784365672276

Offset: 1

Author

Colin Barker, Dec 11 2014

Keywords

• nonn
• easy

Comments

Also nonnegative integers x in the solutions to 2*x^2-5*y^2+4*x+3*y+2+2 = 0, the corresponding values of y being A046195.

Examples

			8 is in the sequence because T(8)+T(9) = 36+45 = 81 = H(6).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..950
• Index entries for linear recurrences with constant coefficients, signature (1,0,1442,-1442,0,-1,1).

Crossrefs

Cf. A000217, A000566, A046195.

Programs

Mathematica

LinearRecurrence[{1,0,1442,-1442,0,-1,1},{0,8,76,1518,12986,111034,2190396},20] (* Harvey P. Dale, Dec 08 2016 *)

PARI

concat(0, Vec(2*x^2*(x^5+4*x^4+34*x^3-721*x^2-34*x-4)/((x-1)*(x^6-1442*x^3+1)) + O(x^100)))

Formula

G.f.: 2*x^2*(x^5+4*x^4+34*x^3-721*x^2-34*x-4) / ((x-1)*(x^6-1442*x^3+1)).