A252586 - OEIS

A252586

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

4, 257, 1772, 123729, 853956, 59636977, 411604876, 28744899041, 198392696132, 13854981700641, 95624867930604, 6678072434809777, 46090987949854852, 3218817058596611729, 22215760566962107916, 1551463144171132043457, 10707950502287786160516

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OFFSET

1,1

COMMENTS

Also positive integers y in the solutions to 6*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of x being A252585.

LINKS

Colin Barker, Table of n, a(n) for n = 1..745

Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).

FORMULA

a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+11*x^3-413*x^2+253*x+4) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).

EXAMPLE

4 is in the sequence because H(4) = 23 = 12+22 = P(3)+P(4).

PROG

(PARI) Vec(-x*(x^4+11*x^3-413*x^2+253*x+4)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))

CROSSREFS

Cf. A000326, A000566, A252585.

Sequence in context: A132656 A137840 A114561 * A214136 A068417 A116967

Adjacent sequences: A252583 A252584 A252585 * A252587 A252588 A252589

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Dec 18 2014

STATUS

approved