A252985 Numbers n such that the sum of the hexagonal numbers X(n) and X(n+1) is equal to the heptagonal number H(m) for some m.

1, 579, 1870, 835278, 2696899, 1204470657, 3888926848, 1736845852476, 5607829818277, 2504530514800095, 8086486709028946, 3611531265495884874, 11660708226589922215, 5207825580314551188573, 16814733176255958805444, 7509680875282317318037752

Offset

1,2

Comments

Also positive integers x in the solutions to 8*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of y being A252986.

Links

Colin Barker, Table of n, a(n) for n = 1..633

Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

Formula

a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(68*x^3+151*x^2-578*x-1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).

Example

1 is in the sequence because X(1)+X(2) = 1+6 = 7 = H(2).

Prog

(PARI) Vec(x*(68*x^3+151*x^2-578*x-1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Crossrefs

Cf. A000384, A000566, A252986.

Sequence in context: A286233 A073735 A250727 * A097769 A186786 A185609

Adjacent sequences: A252982 A252983 A252984 * A252986 A252987 A252988

Keyword

nonn,easy

Author

Colin Barker, Dec 25 2014

Status

approved