A251769 Numbers n such that the sum of the heptagonal numbers H(n), H(n+1) and H(n+2) is equal to the sum of three consecutive squares.

17, 239, 25529, 345647, 36813809, 498423743, 53085488057, 718726692767, 76549236965393, 1036403392547279, 110383946618609657, 1494492973326484559, 159173574474798161009, 2155057831133398187807, 229528184008712329566329, 3107591898001386860334143

Offset

1,1

Comments

Also nonnegative integers x in the solutions to 15*x^2-6*y^2+21*x-12*y+6 = 0, the corresponding values of y being A251770.

Links

Colin Barker, Table of n, a(n) for n = 1..633

Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

Formula

a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(x^4+6*x^3-776*x^2-222*x-17) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).

Example

17 is in the sequence because H(17)+H(18)+H(19) = 697+783+874 = 2354 = 729+784+841 = 27^2+28^2+29^2.

Prog

(PARI) Vec(x*(x^4+6*x^3-776*x^2-222*x-17)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Crossrefs

Cf. A000290, A000566, A251770.

Sequence in context: A125474 A264455 A142126 * A290340 A103772 A196987

Adjacent sequences: A251766 A251767 A251768 * A251770 A251771 A251772

Keyword

nonn,easy

Author

Colin Barker, Dec 08 2014

Status

approved