A375373 -id:A375373 - cp's OEIS frontend

A375372 Expansion of 1/( (1 + x) * (1 - x^2*(1 + x)^2) ).

1, -1, 2, 0, 2, 2, 5, 5, 12, 16, 28, 44, 73, 115, 190, 304, 494, 798, 1293, 2089, 3384, 5472, 8856, 14328, 23185, 37511, 60698, 98208, 158906, 257114, 416021, 673133, 1089156, 1762288, 2851444, 4613732, 7465177, 12078907, 19544086, 31622992, 51167078, 82790070

Offset: 0

Seiichi Manyama, Aug 13 2024

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

Cf. A093040, A375373.

my(N=50, x='x+O('x^N)); Vec(1/((1+x)*(1-x^2*(1+x)^2)))

a(n) = sum(k=0, n\2, binomial(2*k-1, n-2*k));

a(n) = -a(n-1) + a(n-2) + 3*a(n-3) + 3*a(n-4) + a(n-5).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*k-1,n-2*k).
a(n) = A375373(n) + A375373(n-1).
2*a(n) = 2*(-1)^n + A000045(n) + A057078(n+1). - R. J. Mathar, Aug 14 2024

A375371 Expansion of 1/( (1 + x)^2 * (1 - x*(1 + x)^2) ).

Original entry on oeis.org

1, -1, 4, -1, 11, 7, 35, 52, 138, 267, 606, 1266, 2758, 5882, 12679, 27185, 58442, 125473, 269561, 578929, 1243545, 2670942, 5736984, 12322389, 26467324, 56849060, 122106124, 262271540, 563332877, 1209982051, 2598919376, 5582216323, 11990037159, 25753389147

Offset: 0

Seiichi Manyama, Aug 13 2024

sign

Index entries for linear recurrences with constant coefficients, signature (-1,3,6,4,1).

Cf. A375373.

my(N=40, x='x+O('x^N)); Vec(1/((1+x)^2*(1-x*(1+x)^2)))

a(n) = sum(k=0, n, binomial(2*k-2, n-k));

a(n) = -a(n-1) + 3*a(n-2) + 6*a(n-3) + 4*a(n-4) + a(n-5).

a(n) = Sum_{k=0..n} binomial(2*k-2,n-k).

cp's OEIS Frontend

A375372 Expansion of 1/( (1 + x) * (1 - x^2*(1 + x)^2) ).

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A375371 Expansion of 1/( (1 + x)^2 * (1 - x*(1 + x)^2) ).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula