A252077 Numbers n such that the hexagonal number X(n) is equal to the sum of the heptagonal number H(m) and H(m+1) for some m.

1, 769, 1108537, 1598509225, 2305049193553, 3323879338593841, 4793031701203124809, 6911548389255567380377, 9966447984274826959378465, 14371611081775911219856365793, 20723853213472879704205920094681, 29883781962216810757553716920163849

Offset

1,2

Comments

Also nonnegative integers y in the solutions to 10*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of x being A252076.

Links

Colin Barker, Table of n, a(n) for n = 1..317

Index entries for linear recurrences with constant coefficients, signature (1443,-1443,1).

Formula

a(n) = 1443*a(n-1)-1443*a(n-2)+a(n-3).

G.f.: -x*(313*x^2-674*x+1) / ((x-1)*(x^2-1442*x+1)).

Example

769 is in the sequence because X(769) = 1181953 = 589761+592192 = H(486)+H(487).

Prog

(PARI) Vec(-x*(313*x^2-674*x+1)/((x-1)*(x^2-1442*x+1)) + O(x^100))

Crossrefs

Cf. A000384, A000566, A252076.

Sequence in context: A229854 A217495 A216646 * A236784 A205622 A205357

Adjacent sequences: A252074 A252075 A252076 * A252078 A252079 A252080

Keyword

nonn,easy

Author

Colin Barker, Dec 13 2014

Status

approved