A251896 Numbers n such that the octagonal number N(n) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m.

1, 43, 521, 49235, 600849, 56816763, 693378841, 65566494883, 800158581281, 75663678277835, 923382309419049, 87315819166126323, 1065582384911000881, 100762379654031498523, 1229681148804985597241, 116279698804933183168835, 1419050980138568468214849

Offset

1,2

Comments

Also nonnegative integers y in the solutions to 12*x^2-6*y^2+4*x+4*y+2 = 0, the corresponding values of x being A251895.

Links

Colin Barker, Table of n, a(n) for n = 1..653

Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Formula

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(3*x^4+246*x^3-676*x^2+42*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

Example

43 is in the sequence because N(43) = 5461 = 2640+2821 = N(30)+N(31).

Mathematica

LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 43, 521, 49235, 600849}, 20] (* Harvey P. Dale, Aug 25 2024 *)

Prog

(PARI) Vec(-x*(3*x^4+246*x^3-676*x^2+42*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

Crossrefs

Cf. A000567, A251895.

Sequence in context: A238202 A008388 A241939 * A060888 A245427 A337214

Adjacent sequences: A251893 A251894 A251895 * A251897 A251898 A251899

Keyword

nonn,easy

Author

Colin Barker, Dec 10 2014

Status

approved