A251601 Numbers n such that hexagonal numbers H(n) and H(n+1) sum to another hexagonal number.

0, 13, 450, 15295, 519588, 17650705, 599604390, 20368898563, 691942946760, 23505691291285, 798501560956938, 27125547381244615, 921470109401359980, 31302858172264994713, 1063375707747608460270, 36123471205246422654475

Offset

1,2

Comments

Also nonnegative integers x in the solutions to 8*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of y being A251602.

Links

Colin Barker, Table of n, a(n) for n = 1..654

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Formula

a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3).

G.f.: x^2*(5*x-13) / ((x-1)*(x^2-34*x+1)).

a(n) = (-4+(17+12*sqrt(2))^n*(-38+27*sqrt(2))-(17+12*sqrt(2))^(-n)*(38+27*sqrt(2)))/16. - Colin Barker, Mar 02 2016

Example

13 is in the sequence because H(13) + H(14) = 325 + 378 = 703 = H(19).

Prog

(PARI) concat(0, Vec(x^2*(5*x-13)/((x-1)*(x^2-34*x+1)) + O(x^20)))

Crossrefs

Cf. A000384, A251602.

Sequence in context: A012832 A102075 A218586 * A338177 A166184 A272656

Adjacent sequences: A251598 A251599 A251600 * A251602 A251603 A251604

Keyword

nonn,easy

Author

Colin Barker, Dec 05 2014

Status

approved