A252770 Numbers n such that the heptagonal number H(n) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) and P(m+3) for some m.

148, 9155, 567444, 35172355, 2180118548, 135132177603, 8376014892820, 519177791177219, 32180647038094740, 1994680938570696643, 123638037544345097108, 7663563646810825324035, 475017308064726824993044, 29443409536366252324244675, 1825016373946642917278176788

Offset

1,1

Comments

Also positive integers y in the solutions to 12*x^2-5*y^2+32*x+3*y+36 = 0, the corresponding values of x being A252769.

Links

Colin Barker, Table of n, a(n) for n = 1..557

Index entries for linear recurrences with constant coefficients, signature (63,-63,1).

Formula

a(n) = 63*a(n-1)-63*a(n-2)+a(n-3).

G.f.: -x*(3*x^2-169*x+148) / ((x-1)*(x^2-62*x+1)).

Example

148 is in the sequence because H(148) = 54538 = 13207+13490+13776+14065 = P(94)+P(95)+P(96)+P(97).

Prog

(PARI) Vec(-x*(3*x^2-169*x+148)/((x-1)*(x^2-62*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000566, A252769.

Sequence in context: A224372 A185478 A210159 * A035822 A221349 A178083

Adjacent sequences: A252767 A252768 A252769 * A252771 A252772 A252773

Keyword

nonn,easy

Author

Colin Barker, Dec 21 2014

Status

approved