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 1-3 of 3 results.

A225549 a(n) is the number of terms in the expansion of (x-y)*(x^4-y^4)*(x^9-y^9)*...*(x^(n^2)-y^(n^2)).

Original entry on oeis.org

2, 4, 8, 16, 24, 40, 68, 103, 162, 236, 344, 453, 612, 790, 994, 1229, 1432, 1782, 2134, 2517, 2968, 3460, 3974, 4543, 5160, 5822, 6546, 7347, 8184, 9080, 10058, 11075, 12166, 13316, 14536, 15837, 17202, 18654, 20156, 21765, 23450, 25212, 27074, 29001, 31032, 33158, 35370, 37679, 40070, 42578
Offset: 1

Views

Author

Yuval Dekel (dekelyuval(AT)hotmail.com) and Robert G. Wilson v, May 10 2013

Keywords

Comments

In the definition one can take y=1. Thus the sequence becomes the number of terms in the polynomial of the product{k=1..n} (1-x^(k^2)).

Crossrefs

Cf. A000124, A086781, A086795, A086796, A086817.

Programs

  • Mathematica
    a[n_] := Length@ ExpandAll@ Product[(1 - x^(k^2)), {k, n}]; Array[f, 40]
  • PARI
    a(n)=my(P=prod(k=1,n,1-'x^k^2)); sum(i=0, poldegree(P), polcoeff(P,i)!=0) \\ Charles R Greathouse IV, May 10 2013

A221991 a(n) is the number of terms in the expansion of (x-y)(x^2-y^2)*(x^3-y^3)*(x^5-y^5)*...*(x^p_i-y^p_i), where p_i is the i-th prime.

Original entry on oeis.org

2, 4, 6, 8, 10, 20, 22, 36, 42, 66, 90, 110, 142, 184, 232, 284, 342, 400, 458, 532, 604, 678, 756, 838, 928, 1026, 1126, 1230, 1336, 1446, 1558, 1686, 1816, 1954, 2092, 2242, 2392, 2550, 2712, 2880, 3052, 3232, 3412, 3604, 3796, 3994, 4192, 4404, 4626, 4854, 5082
Offset: 1

Views

Author

Robert G. Wilson v, May 12 2013

Keywords

Comments

In the definition one can take y=1. Thus the sequence becomes the number of terms in the polynomial of the product{k=0..n} (1-x^p_i), where p_i is the i-th prime and p_0 = 1.
Offset is 1 to keep it parallel to other like sequences.

Crossrefs

Cf. A000124, A086781, A086795, A086796, A086817, A225549.

Programs

  • Mathematica
    f[n_] := Length@ ExpandAll[(1 - x) Product[(1 - x^Prime[k]), {k, n}]]; Array[f, 51, 0]

A222028 a(n) is the number of terms in the expansion of (x-y)(x^3-y^3)*(x^6-y^6)*(x^10-y^10)*...*(x^T_i-y^T_i), where T_i is the i-th triangular number.

Original entry on oeis.org

2, 4, 8, 15, 28, 41, 66, 92, 132, 175, 232, 287, 360, 475, 570, 727, 852, 1009, 1220, 1397, 1646, 1891, 2154, 2441, 2772, 3121, 3508, 3891, 4334, 4791, 5282, 5797, 6376, 6983, 7618, 8285, 8984, 9713, 10500, 11319, 12182, 13093, 14028, 15023, 16064, 17157, 18276, 19447, 20680, 21953
Offset: 1

Views

Author

Robert G. Wilson v, May 12 2013

Keywords

Comments

In the definition one can take y=1. Thus the sequence becomes the number of terms in the polynomial of the product{k=0..n} (1-x^T_i), where G_i is the i-th triangular number.

Crossrefs

Cf. A000124, A086781, A086795, A086796, A086817, A221991, A225549.

Programs

  • Mathematica
    f[n_] := Length@ ExpandAll@ Product[1 - x^(k (k + 1)/2), {k, n}]; Array[f, 50]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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