A251793 Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m.

0, 2, 68, 286, 6760, 28122, 662508, 2755766, 64919120, 270037042, 6361411348, 26460874446, 623353393080, 2592895658762, 61082271110588, 254077313684326, 5985439215444640, 24896983845405282, 586511960842464228, 2439650339536033406

Offset

1,2

Comments

Also nonnegative integers y in the solutions to 6*x^2-y^2+2*x-2*y = 0, the corresponding values of x being A220755.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).

Formula

a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).

G.f.: -2*x^2*(3*x^3+11*x^2+33*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

Example

68 is in the sequence because T(68)+T(69) = 2346+2415 = 4761 = 2296+2465 = N(28)+N(29).

Prog

(PARI) concat(0, Vec(-2*x^2*(3*x^3+11*x^2+33*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100)))

Crossrefs

Cf. A000217, A000567, A220755.

Sequence in context: A202606 A304044 A355493 * A283038 A264457 A246744

Adjacent sequences: A251790 A251791 A251792 * A251794 A251795 A251796

Keyword

nonn,easy

Author

Colin Barker, Dec 09 2014

Status

approved