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.

A274622 Irregular triangular array read by rows: coefficients in expansion of Gosper's q-sine function sin_q(Pi*z).

Original entry on oeis.org

1, 1, 2, 2, 1, 4, 4, 1, 2, 8, 8, 2, 4, 14, 14, 4, 8, 24, 24, 8, 1, 14, 40, 40, 14, 1, 2, 24, 64, 64, 24, 2, 4, 40, 100, 100, 40, 4, 8, 64, 154, 154, 64, 8, 14, 100, 232, 232, 100, 14, 24, 154, 344, 344, 154, 24, 1, 40, 232, 504, 504, 232, 40, 1, 2, 64, 344, 728, 728, 344, 64, 2, 4, 100, 504, 1040, 1040, 504, 100, 4
Offset: 0

Views

Author

N. J. A. Sloane, Jul 04 2016

Keywords

Examples

			The array begins:
.........1,1,
.........2,2,
.......1,4,4,1,
.......2,8,8,2,
.......4,14,14,4,
.......8,24,24,8,
....1,14,40,40,14,1,
....2,24,64,64,24,2,
....4,40,100,100,40,4,
....8,64,154,154,64,8,
....14,100,232,232,100,14,
....24,154,344,344,154,24,
..1,40,232,504,504,232,40,1,
..2,64,344,728,728,344,64,2,
..4,100,504,1040,1040,504,100,4,
...

References

  • R. W. Gosper, Experiments and discoveries in q-trigonometry, in Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics. Editors: F. G. Garvan and M. E. H. Ismail. Kluwer, Dordrecht, Netherlands, 2001, pp. 79-105.

Links

Crossrefs

Cf. A274623, A274624, A274625.

Programs

  • Mathematica
    nmax = 14; kmax = 4; QP = QPochhammer; s = QP[q^2]/QP[q]^2 + O[q]^(nmax + 1); col[1] = CoefficientList [s, q]; col[k_] := Join[Array[0&, k(k-1)], Take[col[1], nmax-k(k-1)+1]]; T = Transpose[Array[col, kmax]]; ro[n_] := DeleteCases[T[[n+1]], 0]; row[n_] := Join[Reverse[ro[n]], ro[n]]; Table[row[n], {n, 0, nmax}] // Flatten (* Jean-François Alcover, Oct 07 2016 *)

A274624 Irregular triangular array read by rows: coefficients in expansion of Gosper's q-cosine function cos_q(Pi*z).

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 2, 4, 8, 4, 1, 8, 14, 8, 1, 2, 14, 24, 14, 2, 4, 24, 40, 24, 4, 8, 40, 64, 40, 8, 14, 64, 100, 64, 14, 1, 24, 100, 154, 100, 24, 1, 2, 40, 154, 232, 154, 40, 2, 4, 64, 232, 344, 232, 64, 4, 8, 100, 344, 504, 344, 100, 8, 14, 154, 504, 728, 504, 154, 14, 24, 232, 728, 1040, 728, 232, 24
Offset: 0

Views

Author

N. J. A. Sloane, Jul 05 2016

Keywords

Examples

			The array begins:
.........1,
.......1,2,1,
.......2,4,2,
.......4,8,4,
.....1,8,14,8,1,
....2,14,24,14,2,
....4,24,40,24,4,
....8,40,64,40,8,
...14,64,100,64,14,
.1,24,100,154,100,24,1,
.2,40,154,232,154,40,2,
.4,64,232,344,232,64,4,
.8,100,344,504,344,100,8,
14,154,504,728,504,154,14,
24,232,728,1040,728,232,24,
...

References

  • R. W. Gosper, Experiments and discoveries in q-trigonometry, in Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics. Editors: F. G. Garvan and M. E. H. Ismail. Kluwer, Dordrecht, Netherlands, 2001, pp. 79-105.

Links

Crossrefs

Cf. A274622, A274623, A274625.

A274625 Right half plus central column of triangular array in A274624.

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 8, 1, 8, 14, 2, 14, 24, 4, 24, 40, 8, 40, 64, 14, 64, 100, 1, 24, 100, 154, 2, 40, 154, 232, 4, 64, 232, 344, 8, 100, 344, 504, 14, 154, 504, 728, 24, 232, 728, 1040
Offset: 0

Views

Author

N. J. A. Sloane, Jul 05 2016

Keywords

Comments

See A274624, which is the main entry for this array, for further information.

Examples

			Triangle begins:
1,
1,2,
2,4,
4,8,
1,8,14,
2,14,24,
4,24,40,
8,40,64,
14,64,100,
1,24,100,154,
2,40,154,232,
4,64,232,344,
8,100,344,504,
14,154,504,728,
24,232,728,1040,
...

Crossrefs

Cf. A274622, A274623, A274624.
Showing 1-3 of 3 results.

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

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