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 1-5 of 5 results.

A284499 Expansion of Product_{k>=0} (1 - x^(7*k+1)) in powers of x.

Original entry on oeis.org

1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, -1, 3, -2, 0, 0, 0, 0, -1, 3, -3, 1, 0, 0, 0, -1, 4, -4, 1, 0, 0, 0, -1, 4, -5, 2, 0, 0, 0, -1, 5, -7, 3, 0, 0, 0, -1, 5, -8, 5, -1, 0, 0, -1, 6, -10
Offset: 0

Views

Author

Seiichi Manyama, Mar 28 2017

Keywords

Links

Crossrefs

Cf. Product_{k>=0} (1 - x^(7*k+m)): this sequence (m=1), A284500 (m=2), A284501 (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).
Cf. A280457.

Programs

  • Maple
    G:= mul(1-x^(7*k+1),k=0..100/7):
S:= series(G,x,101):
seq(coeff(S,x,j),j=0..100); # Robert Israel, Mar 29 2017
  • Mathematica
    CoefficientList[Series[Product[1 - x^(7k + 1), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 28 2017 *)
  • PARI
    Vec(prod(k=0, 100, 1 - x^(7*k + 1)) + O(x^101)) \\ Indranil Ghosh, Mar 28 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284099(k)*a(n-k), a(0) = 1.

A284500 Expansion of Product_{k>=0} (1 - x^(7*k+2)) in powers of x.

Original entry on oeis.org

1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 2, 0, -1, 0, 0, -1, 0, 2, 0, -1, 0, 0, -1, 0, 3, 0, -2, 0, 0, -1, 0, 3, 0, -3, 0, 1, -1, 0, 4, 0, -4, 0, 1, -1, 0, 4, 0, -5, 0, 2, -1, 0, 5, 0, -7, 0, 3, -1, 0, 5, 0, -8, 0, 5, -1, -1
Offset: 0

Views

Author

Seiichi Manyama, Mar 28 2017

Keywords

Links

Crossrefs

Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), this sequence (m=2), A284501 (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).
Cf. A281458.

Programs

  • Maple
    S:= series(mul(1-x^(7*k+2),k=0..(100-2)/7),x,101):
seq(coeff(S,x,i),i=0..100); # Robert Israel, Jan 17 2023
  • Mathematica
    CoefficientList[Series[Product[1 - x^(7k + 2), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 28 2017 *)
  • PARI
    Vec(prod(k=0, 100, 1 - x^(7*k + 2)) + O(x^101)) \\ Indranil Ghosh, Mar 28 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284443(k)*a(n-k), a(0) = 1.

A284501 Expansion of Product_{k>=0} (1 - x^(7*k+3)) in powers of x.

Original entry on oeis.org

1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, -1, 0, 0, 2, 0, 0, -1, -1, 0, 0, 3, 0, 0, -2, -1, 0, 0, 3, 0, 0, -3, -1, 0, 1, 4, 0, 0, -4, -1, 0, 1, 4, 0, 0, -5, -1, 0, 2, 5, 0, 0, -7, -1, 0, 3, 5, 0, 0, -8, -1, 0, 5
Offset: 0

Views

Author

Seiichi Manyama, Mar 28 2017

Keywords

Links

Crossrefs

Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), A284500 (m=2), this sequence (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).
Cf. A281457.

Programs

  • Mathematica
    CoefficientList[Series[Product[1 - x^(7k + 3), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 28 2017 *)
  • PARI
    Vec(prod(k=0, 100, 1 - x^(7*k + 3)) + O(x^101)) \\ Indranil Ghosh, Mar 28 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284444(k)*a(n-k), a(0) = 1.

A284502 Expansion of Product_{k>=0} (1 - x^(7*k+4)) in powers of x.

Original entry on oeis.org

1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, -1, -1, 0, 0, 2, 0, 0, -1, -1, 0, 0, 3, 0, 0, -1, -2, 0, 0, 3, 0, 0, -1, -3, 0, 0, 4, 1, 0, -1, -4, 0, 0, 4, 1, 0, -1, -5, 0, 0, 5, 2, 0, -1, -7, 0, 0, 5, 3, 0, -1, -8
Offset: 0

Views

Author

Seiichi Manyama, Mar 28 2017

Keywords

Links

Crossrefs

Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), A284500 (m=2), A284501 (m=3), this sequence (m=4), A284503 (m=5), A284504 (m=6).
Cf. A281456.

Programs

  • Mathematica
    CoefficientList[Series[Product[1 - x^(7k + 4), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 28 2017 *)
  • PARI
    Vec(prod(k=0, 100, 1 - x^(7*k + 4)) + O(x^101)) \\ Indranil Ghosh, Mar 28 2017

Formula

a(n) = -(1/n) * Sum_{k=1..n} A284445(k) * a(n-k), a(0) = 1.

A284503 Expansion of Product_{k>=0} (1 - x^(7*k+5)) in powers of x.

Original entry on oeis.org

1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0, 2, 0, -1, 0, 0, -1, 0, 3, 0, -1, 0, 0, -2, 0, 3, 0, -1, 0, 0, -3, 0, 4, 0, -1, 1, 0, -4, 0, 4, 0, -1, 1, 0, -5, 0, 5, 0, -1, 2, 0, -7, 0, 5, 0
Offset: 0

Views

Author

Seiichi Manyama, Mar 28 2017

Keywords

Links

Crossrefs

Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), A284500 (m=2), A284501 (m=3), A284502 (m=4), this sequence (m=5), A284504 (m=6).
Cf. A281455.

Programs

  • Mathematica
    CoefficientList[Series[Product[1 - x^(7k + 5), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 28 2017  *)
  • PARI
    Vec(prod(k=0, 100, 1 - x^(7*k + 5)) + O(x^101)) \\ Indranil Ghosh, Mar 28 2017

Formula

a(n) = -(1/n) * Sum_{k=1..n} A284446(k) * a(n-k), a(0) = 1.
Showing 1-5 of 5 results.

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