cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A376726 Expansion of (1 + x^2 - x^3)/((1 + x^2 - x^3)^2 - 4*x^2).

Original entry on oeis.org

1, 0, 3, 1, 5, 10, 8, 35, 30, 85, 137, 201, 476, 616, 1357, 2172, 3735, 7193, 11213, 21782, 36064, 64095, 115130, 193769, 354737, 604049, 1074008, 1889968, 3273785, 5839608, 10106859, 17880785, 31325077, 54793282, 96710296, 168730043, 297336790, 520856765, 913684857
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2024

Keywords

Links

Crossrefs

Cf. A099511, A376727, A376728.
Cf. A376723, A376729.

Programs

  • PARI
    my(N=40, x='x+O('x^N)); Vec((1+x^2-x^3)/((1+x^2-x^3)^2-4*x^2))
  • PARI
    a(n) = sum(k=0, n\2, binomial(2*k+1, 2*n-4*k+1));

Formula

a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*k+1,2*n-4*k+1).

A376727 Expansion of (1 + x^3 - x^4)/((1 + x^3 - x^4)^2 - 4*x^3).

Original entry on oeis.org

1, 0, 0, 3, 1, 0, 5, 10, 1, 7, 35, 21, 10, 84, 126, 47, 166, 462, 343, 341, 1288, 1731, 1170, 3081, 6453, 5685, 7553, 19572, 25280, 24004, 52789, 93844, 95932, 143435, 299577, 386536, 448673, 873754, 1411193, 1625003, 2536215, 4639077, 6097214, 7959492, 14238226
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2024

Keywords

Links

Crossrefs

Cf. A099511, A376726, A376728.
Cf. A376724, A376730.

Programs

  • PARI
    my(N=50, x='x+O('x^N)); Vec((1+x^3-x^4)/((1+x^3-x^4)^2-4*x^3))
  • PARI
    a(n) = sum(k=0, n\3, binomial(2*k+1, 2*n-6*k+1));

Formula

a(n) = 2*a(n-3) + 2*a(n-4) - a(n-6) + 2*a(n-7) - a(n-8).
a(n) = Sum_{k=0..floor(n/3)} binomial(2*k+1,2*n-6*k+1).

A376731 Expansion of (1 - x^4 - x^5)/((1 - x^4 - x^5)^2 - 4*x^9).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 0, 0, 1, 6, 1, 0, 1, 15, 15, 1, 1, 28, 70, 28, 2, 45, 210, 210, 46, 67, 495, 924, 496, 157, 1002, 3003, 3004, 1121, 1911, 8009, 12871, 8161, 4880, 18684, 43760, 43948, 23409, 41820, 126124, 184988, 133285, 113373, 324616, 647112, 657273, 454366
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2024

Keywords

Links

Crossrefs

Cf. A108479, A376729, A376730.
Cf. A376725, A376728.

Programs

  • PARI
    my(N=60, x='x+O('x^N)); Vec((1-x^4-x^5)/((1-x^4-x^5)^2-4*x^9))
  • PARI
    a(n) = sum(k=0, n\4, binomial(2*k, 2*n-8*k));

Formula

a(n) = 2*a(n-4) + 2*a(n-5) - a(n-8) + 2*a(n-9) - a(n-10).
a(n) = Sum_{k=0..floor(n/4)} binomial(2*k,2*n-8*k).

A376725 Expansion of 1/((1 - x^4 - x^5)^2 - 4*x^9).

Original entry on oeis.org

1, 0, 0, 0, 2, 2, 0, 0, 3, 10, 3, 0, 4, 28, 28, 4, 5, 60, 126, 60, 11, 110, 396, 396, 117, 188, 1001, 1716, 1009, 462, 2191, 5720, 5729, 2592, 4564, 15920, 24320, 16482, 12036, 39168, 84000, 84750, 51927, 93024, 249292, 353738, 269962, 258324, 666932, 1250142
Offset: 0

Views

Author

Seiichi Manyama, Oct 02 2024

Keywords

Links

Crossrefs

Cf. A182890, A376723, A376724.
Cf. A376728, A376731.

Programs

  • PARI
    my(N=50, x='x+O('x^N)); Vec(1/((1-x^4-x^5)^2-4*x^9))
  • PARI
    a(n) = sum(k=0, n\4, binomial(2*k+2, 2*n-8*k+1))/2;

Formula

a(n) = 2*a(n-4) + 2*a(n-5) - a(n-8) + 2*a(n-9) - a(n-10).
a(n) = (1/2) * Sum_{k=0..floor(n/4)} binomial(2*k+2,2*n-8*k+1).
Showing 1-4 of 4 results.

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