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.

A292140 G.f.: Im((2*i; x)_oo), where (a; q)_oo is the q-Pochhammer symbol, i = sqrt(-1).

Original entry on oeis.org

-2, -2, -2, 6, 6, 14, 22, 30, 38, 54, 30, 46, 30, 14, -34, -74, -154, -226, -362, -498, -698, -762, -1058, -1218, -1474, -1634, -1890, -1914, -2074, -2002, -1962, -1570, -1210, -266, 606, 2190, 3454, 6030, 8382, 11926, 15334, 20190, 24758, 30990, 36678, 44134
Offset: 0

Views

Author

Seiichi Manyama, Sep 09 2017

Keywords

Links

Crossrefs

Column k=2 of A292160.
Cf. A278400, A292135, A292141.

Formula

(2*i; x)_oo is the g.f. for A292135(n) + i*a(n).

A292159 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Re((k*i; x)_inf), and (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

Original entry on oeis.org

1, 1, 0, 1, -1, 0, 1, -4, -1, 0, 1, -9, -4, -2, 0, 1, -16, -9, -8, -2, 0, 1, -25, -16, -18, -8, -3, 0, 1, -36, -25, -32, -18, -12, -2, 0, 1, -49, -36, -50, -32, -27, 4, -3, 0, 1, -64, -49, -72, -50, -48, 54, 0, -2, 0, 1, -81, -64, -98, -72, -75, 208, 45, 16, -2
Offset: 0

Views

Author

Seiichi Manyama, Sep 10 2017

Keywords

Examples

			Square array begins:
   1,  1,  1,   1,   1, ...
   0, -1, -4,  -9, -16, ...
   0, -1, -4,  -9, -16, ...
   0, -2, -8, -18, -32, ...
   0, -2, -8, -18, -32, ...

Links

Crossrefs

Columns k=0..2 give A000007, A278399, A292135.
Rows n=0..1 give A000012, (-1)*A000290.
Main diagonal gives A292161.
Cf. A292160.

A292142 Triangle read by rows: T(n,k) = (-4)^(k mod 2) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

Original entry on oeis.org

1, 0, -4, 0, -4, 0, -4, -4, 0, -4, -4, 0, -4, -8, 0, -4, -8, 16, 0, -4, -12, 16, 0, -4, -12, 32, 0, -4, -16, 48, 0, -4, -16, 64, 16, 0, -4, -20, 80, 16, 0, -4, -20, 112, 32, 0, -4, -24, 128, 48, 0, -4, -24, 160, 80, 0, -4, -28, 192, 96, -64, 0, -4, -28, 224, 144
Offset: 0

Views

Author

Seiichi Manyama, Sep 09 2017

Keywords

Examples

			First few rows are:
  1;
  0, -4;
  0, -4;
  0, -4,  -4;
  0, -4,  -4;
  0, -4,  -8;
  0, -4,  -8, 16;
  0, -4, -12, 16;
  0, -4, -12, 32;
  0, -4, -16, 48;
  0, -4, -16, 64, 16.

Links

Crossrefs

Row sums give A292135.
Columns 0-1 give A000007, (-4)*A000012.
Cf. A292047.
Showing 1-3 of 3 results.

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

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