A251602 Numbers n such that hexagonal number H(n) is the sum of two consecutive hexagonal numbers.

1, 19, 637, 21631, 734809, 24961867, 847968661, 28805972599, 978555099697, 33242067417091, 1129251737081389, 38361316993350127, 1303155526036822921, 44268926568258629179, 1503840347794756569157, 51086302898453464722151, 1735430458199623043983969

Offset

1,2

Comments

Also nonnegative integers y in the solutions to 8*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of x being A251601.

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*(7*x^2-16*x+1) / ((x-1)*(x^2-34*x+1)).

a(n) = (2+(27-19*sqrt(2))*(17+12*sqrt(2))^n+(17+12*sqrt(2))^(-n)*(27+19*sqrt(2)))/8. - Colin Barker, Mar 02 2016

Example

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

Prog

(PARI) Vec(-x*(7*x^2-16*x+1)/((x-1)*(x^2-34*x+1)) + O(x^20))

Crossrefs

Cf. A000384, A251601.

Sequence in context: A290007 A119555 A107118 * A217824 A217825 A200849

Adjacent sequences: A251599 A251600 A251601 * A251603 A251604 A251605

Keyword

nonn,easy

Author

Colin Barker, Dec 05 2014

Status

approved