A252631 Numbers n such that the heptagonal number H(n) is equal to the sum of the hexagonal numbers X(m), X(m+1), X(m+2) and X(m+3) for some m.

92, 29524, 9506540, 3061076260, 985657049084, 317378508728692, 102194894153589644, 32906438538947136580, 10595771014646824389020, 3411805360277738506127764, 1098590730238417152148750892, 353742803331410045253391659364, 113904084081983796154439965564220

Offset

1,1

Comments

Also positive integers y in the solutions to 16*x^2-5*y^2+40*x+3*y+44 = 0, the corresponding values of x being A252630.

Links

Colin Barker, Table of n, a(n) for n = 1..398

Index entries for linear recurrences with constant coefficients, signature (323,-323,1).

Formula

a(n) = 323*a(n-1)-323*a(n-2)+a(n-3).

G.f.: -4*x*(x^2-48*x+23) / ((x-1)*(x^2-322*x+1)).

a(n) = (6+(37+14*sqrt(5))*(161+72*sqrt(5))^(-n)+(37-14*sqrt(5))*(161+72*sqrt(5))^n)/20. - Colin Barker, Mar 03 2016

Example

92 is in the sequence because H(92) = 21022 = 4950+5151+5356+5565 = X(50)+X(51)+X(52)+X(53).

Prog

(PARI) Vec(-4*x*(x^2-48*x+23)/((x-1)*(x^2-322*x+1)) + O(x^100))

Crossrefs

Cf. A000384, A000566, A252630.

Sequence in context: A146503 A252593 A146515 * A191948 A278860 A283897

Adjacent sequences: A252628 A252629 A252630 * A252632 A252633 A252634

Keyword

nonn,easy

Author

Colin Barker, Dec 19 2014

Status

approved