

A252630


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


2



50, 16503, 5314316, 1711193649, 550999041062, 177419980028715, 57128682570205568, 18395258367626164581, 5923216065693054789914, 1907257177894796016188127, 614130888066058624157787380, 197748238700092982182791348633, 63674318730541874204234656472846
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OFFSET

1,1


COMMENTS

Also positive integers x in the solutions to 16*x^25*y^2+40*x+3*y+44 = 0, the corresponding values of y being A252631.


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(n1)323*a(n2)+a(n3).
G.f.: x*(3*x^2353*x50) / ((x1)*(x^2322*x+1)).
a(n) =5/4+1/80*(161+72*sqrt(5))^(n)*(7037*sqrt(5)+(70+37*sqrt(5))*(161+72*sqrt(5))^(2*n)).  Colin Barker, Mar 03 2016


EXAMPLE

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


PROG

(PARI) Vec(x*(3*x^2353*x50)/((x1)*(x^2322*x+1)) + O(x^100))


CROSSREFS

Cf. A000384, A000566, A252631.
Sequence in context: A152258 A203097 A028465 * A034205 A173170 A146518
Adjacent sequences: A252627 A252628 A252629 * A252631 A252632 A252633


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Dec 19 2014


STATUS

approved



