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

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