A322753 Expansion of x*(1 + 2*x - 3*x^2 + 4*x^3) / (1 - x - x^2 + x^3 - x^4).

0, 1, 3, 1, 7, 6, 15, 15, 31, 37, 68, 89, 151, 209, 339, 486, 767, 1123, 1743, 2585, 3972, 5937, 9067, 13617, 20719, 31206, 47375, 71479, 108367, 163677, 247940, 374729, 567359, 857825, 1298395, 1963590, 2971519, 4494539, 6800863, 10287473, 15565316

Offset

0,3

References

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 48.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) for n>4. - Colin Barker, Jan 06 2019

Mathematica

CoefficientList[Series[(x + 2*x^2 - 3*x^3 + 4*x^4)/(1 - x - x^2 + x^3 - x^4), {x, 0, 50}], x] (* Amiram Eldar, Jan 11 2019 *)
LinearRecurrence[{1, 1, -1, 1}, {0, 1, 3, 1, 7}, 50] (* Harvey P. Dale, Jan 29 2023 *)

Prog

(PARI) concat(0, Vec(x*(1 + 2*x - 3*x^2 + 4*x^3) / (1 - x - x^2 + x^3 - x^4) + O(x^50))) \\ Colin Barker, Jan 06 2019

Crossrefs

Sequence in context: A359079 A245684 A082053 * A136035 A132307 A372968

Adjacent sequences: A322750 A322751 A322752 * A322754 A322755 A322756

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 25 2018

Status

approved