A251895 Numbers n such that the sum of the octagonal numbers N(n) and N(n+1) is equal to another octagonal number.

0, 30, 368, 34814, 424864, 40175518, 490292880, 46362513150, 565797558848, 53502299999774, 652929892617904, 61741607837226238, 753480530283502560, 71249761941859079070, 869515879017269336528, 82222163539297540020734, 1003420570905398530850944

Offset

1,2

Comments

Also nonnegative integers x in the solutions to 12*x^2-6*y^2+4*x+4*y+2 = 0, the corresponding values of y being A251896.

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.: 2*x^2*(x^3+87*x^2-169*x-15) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

Example

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

Prog

(PARI) concat(0, Vec(2*x^2*(x^3+87*x^2-169*x-15)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100)))

Crossrefs

Cf. A000567, A251896.

Sequence in context: A058837 A042748 A202074 * A022690 A224332 A280478

Adjacent sequences: A251892 A251893 A251894 * A251896 A251897 A251898

Keyword

nonn,easy

Author

Colin Barker, Dec 10 2014

Status

approved