A251770 Numbers n such that n^2 + (n+1)^2 + (n+2)^2 is equal to the sum of the heptagonal numbers H(m), H(m+1) and H(m+2) for some m.

27, 378, 40365, 546516, 58207743, 788077134, 83935526481, 1136406682152, 121034970979299, 1638697647587490, 174532344216624117, 2363000871414479868, 251675519325400998855, 3407445617882032383606, 362915924334884023726233

Offset

1,1

Comments

Also nonnegative integers y in the solutions to 15*x^2-6*y^2+21*x-12*y+6 = 0, the corresponding values of x being A251769.

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.: -9*x*(x^3+117*x^2+39*x+3) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).

Example

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

Mathematica

LinearRecurrence[{1, 1442, -1442, -1, 1}, {27, 378, 40365, 546516, 58207743}, 20] (* Harvey P. Dale, Jan 28 2020 *)

Prog

(PARI) Vec(-9*x*(x^3+117*x^2+39*x+3)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Crossrefs

Cf. A000290, A000566, A251769.

Sequence in context: A022591 A321954 A000535 * A033280 A125462 A326605

Adjacent sequences: A251767 A251768 A251769 * A251771 A251772 A251773

Keyword

nonn,easy

Author

Colin Barker, Dec 08 2014

Status

approved