A349201 a(n) = [x^n] ((x^2*(1 + 3*x + x^2 - 2*x^3 + 3*x^4 + x^5 - x^6))/((-1 + x)^4 *(1 + x)^3)).

0, 1, 4, 8, 15, 27, 40, 64, 85, 125, 156, 216, 259, 343, 400, 512, 585, 729, 820, 1000, 1111, 1331, 1464, 1728, 1885, 2197, 2380, 2744, 2955, 3375, 3616, 4096, 4369, 4913, 5220, 5832, 6175, 6859, 7240, 8000, 8421, 9261, 9724, 10648, 11155, 12167, 12720, 13824

Offset

1,3

Comments

A subsequence of A348897, i.e. each term of this sequence has the form (x + y)*(x^2 + y^2).

Links

Table of n, a(n) for n=1..48.

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

From Stefano Spezia, Nov 11 2021: (Start)

a(n) = ((5 + 3*n - n^2)*(1 - (-1)^n) + 2*n^3)/16 for n > 1.

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4)+ 3*a(n-5) + a(n-6) - a(n-7) for n > 8. (End)

Mathematica

Join[{0}, LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 4, 8, 15, 27, 40, 64}, 47]] (* Stefano Spezia, Nov 11 2021 *)

Crossrefs

Cf. A348897.

Sequence in context: A098196 A027961 A348897 * A301203 A018921 A305218

Adjacent sequences: A349198 A349199 A349200 * A349202 A349203 A349204

Keyword

nonn,easy

Author

Peter Luschny, Nov 10 2021

Status

approved