A251624 Numbers n such that the octagonal numbers N(n), N(n+1) and N(n+2) sum to another octagonal number.

278, 752958, 2034494038, 5497202139518, 14853438146485398, 40133984374601407678, 108442010926734857062358, 293010273390053209181085438, 791713650257912844472435792918, 2139209989986607115711312331380798, 5780144601230162168739121446955125078

Offset

1,1

Comments

Also nonnegative integers x in the solutions to 18*x^2-6*y^2+24*x+4*y+18 = 0, the corresponding values of y being A251625.

It seems that the least significant digit of each term is 8.

Links

Colin Barker, Table of n, a(n) for n = 1..291

Index entries for linear recurrences with constant coefficients, signature (2703,-2703,1).

Formula

a(n) = 2703*a(n-1)-2703*a(n-2)+a(n-3).

G.f.: 2*x*(x^2-762*x-139) / ((x-1)*(x^2-2702*x+1)).

a(n) = 2*(-3 - (2*sqrt(3)+3)*(1351+780*sqrt(3))^(-n) + (2*sqrt(3)-3)*(1351+780*sqrt(3))^n) / 9. - Colin Barker, May 30 2017

Example

278 is in the sequence because N(278)+N(279)+N(280) = 231296+232965+234640 = 698901 = N(483).

Mathematica

LinearRecurrence[{2703, -2703, 1}, {278, 752958, 2034494038}, 20] (* Harvey P. Dale, Feb 14 2015 *)

Prog

(PARI) Vec(2*x*(x^2-762*x-139)/((x-1)*(x^2-2702*x+1)) + O(x^100))

Crossrefs

Cf. A000567, A251625.

Sequence in context: A056995 A228135 A188446 * A062384 A053345 A032505

Adjacent sequences: A251621 A251622 A251623 * A251625 A251626 A251627

Keyword

nonn,easy

Author

Colin Barker, Dec 06 2014

Status

approved