A252585 Numbers n such that the sum of the pentagonal numbers P(n) and P(n+1) is equal to the heptagonal number H(m) for some m.

3, 234, 1617, 112948, 779551, 54440862, 375742125, 26240382696, 181106924859, 12647810018770, 87293162040073, 6096218188664604, 42075122996390487, 2938364519126320518, 20280121991098174821, 1416285602000697825232, 9774976724586323873395

Offset

1,1

Comments

Also positive integers x in the solutions to 6*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of y being A252586.

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*(11*x^3+63*x^2-231*x-3) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).

Example

3 is in the sequence because P(3)+P(4) = 12+22 = 34 = H(4).

Mathematica

LinearRecurrence[{1, 482, -482, -1, 1}, {3, 234, 1617, 112948, 779551}, 20] (* Jean-François Alcover, Nov 13 2017 *)

Prog

(PARI) Vec(x*(11*x^3+63*x^2-231*x-3)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000566, A252586.

Sequence in context: A065580 A072320 A162603 * A339751 A053970 A298277

Adjacent sequences: A252582 A252583 A252584 * A252586 A252587 A252588

Keyword

nonn,easy

Author

Colin Barker, Dec 18 2014

Status

approved