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.

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A014747 Theta series of lattice D20+.

Original entry on oeis.org

1, 0, 760, 0, 77560, 524288, 2508000, 10485760, 34729720, 99614720, 259114704, 608174080, 1327461600, 2739404800, 5341699520, 9921626112, 17701924600, 30592204800, 51294999960, 83277905920, 131880275664
Offset: 0

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Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

Links

Crossrefs

Cf. A022051.

Programs

  • Mathematica
    terms = 21; s = 1/2 (EllipticTheta[2, 0, q]^20 + EllipticTheta[3, 0, q]^20 + EllipticTheta[4, 0, q]^20) + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 07 2017 *)

Formula

G.f.: (theta2(q)^20 + theta3(q)^20 + theta4(q)^20)/2.

A297331 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of (theta_3(q^(1/2))^k + theta_4(q^(1/2))^k)/2.

Original entry on oeis.org

1, 1, 0, 1, 0, 0, 1, 4, 2, 0, 1, 12, 4, 0, 0, 1, 24, 6, 0, 0, 0, 1, 40, 24, 24, 4, 0, 0, 1, 60, 90, 96, 12, 8, 0, 0, 1, 84, 252, 240, 24, 24, 0, 0, 0, 1, 112, 574, 544, 200, 144, 8, 0, 2, 0, 1, 144, 1136, 1288, 1020, 560, 96, 48, 4, 0, 0, 1, 180, 2034, 3136, 3444, 1560, 400, 192, 6, 4, 0, 0
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 28 2017

Keywords

Examples

			Square array begins:
1,  1,  1,   1,    1,    1,  ...
0,  0,  4,  12,   24,   40,  ...
0,  2,  4,   6,   24,   90,  ...
0,  0,  0,  24,   96,  240,  ...
0,  0,  4,  12,   24,  200,  ...
0,  0,  8,  24,  144,  560,  ...

Links

Crossrefs

Columns k=0..32 give A000007, A089798 (absolute values), A004018, A004015, A004011, A005930, A008428, A008429, A008430, A008431, A008432, A022042, A022043, A022044, A022045, A022046, A022047, A022048, A022049, A022050, A022051, A022052, A022053, A022054, A022055, A022056, A022057, A022058, A022059, A022060, A022061, A022062, A022063.
Main diagonal gives A303333.
Cf. A122141, A286815.

Programs

  • Mathematica
    Table[Function[k, SeriesCoefficient[(EllipticTheta[3, 0, q^(1/2)]^k + EllipticTheta[4, 0, q^(1/2)]^k)/2, {q, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten

Formula

G.f. of column k: (theta_3(q^(1/2))^k + theta_4(q^(1/2))^k)/2, where theta_() is the Jacobi theta function.
Showing 1-2 of 2 results.

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

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