A252986 Numbers n such that the heptagonal number H(n) is equal to the sum of the hexagonal numbers X(m) and X(m+1) for some m.

2, 733, 2366, 1056553, 3411338, 1523548261, 4919146598, 2196955535377, 7093405982546, 3168008358464941, 10228686507684302, 4568265855950909113, 14749758850674780506, 6587436196272852475573, 21269142033986525804918, 9499078426759597318866721

Offset

1,1

Comments

Also positive integers y in the solutions to 8*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of x being A252985.

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*(x^4+85*x^3-1251*x^2+731*x+2) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).

Example

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

Prog

(PARI) Vec(-x*(x^4+85*x^3-1251*x^2+731*x+2)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Crossrefs

Cf. A000384, A000566, A252985.

Sequence in context: A109949 A375956 A151591 * A247080 A145124 A102969

Adjacent sequences: A252983 A252984 A252985 * A252987 A252988 A252989

Keyword

nonn,easy

Author

Colin Barker, Dec 25 2014

Status

approved