A007328 -id:A007328 - cp's OEIS frontend

A007326 Difference between A000294 and the number of solid partitions of n (A000293).

0, 0, 0, 0, 0, 0, 1, 3, 8, 19, 40, 83, 176, 365, 775, 1643, 3483, 7299, 15170, 31010, 62563, 124221, 243296, 469856, 896491, 1690475, 3155551, 5834871, 10701036, 19479021, 35227889, 63335778, 113286272, 201687929, 357585904, 631574315, 1111614614, 1950096758, 3410420973, 5946337698, 10337420278, 17918573379, 30968896662, 53366449357, 91689380979, 157058043025, 268210414468, 456613323892

Offset: 0

N. J. A. Sloane, Mira Bernstein

nonn

Understanding this sequence is a famous unsolved problem in the theory of partitions.

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 190.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vaclav Kotesovec, Table of n, a(n) for n = 0..72
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100.
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]

a(n) = A000294(n) - A000293(n).

Cf. A007327, A007328, A007329, A007330, A008780, A042984.

Entry revised by Sean A. Irvine and N. J. A. Sloane, Dec 18 2017

A007327 Difference between two partition g.f.s.

Original entry on oeis.org

0, 0, 0, 0, 0, 5, 20, 69, 200, 521, 1294, 3126, 7364, 17309, 40577, 95460, 224971, 531368, 1252664, 2943095, 6870029, 15911618, 36507381, 82930347, 186414619, 414654766, 912766795, 1989007381, 4292038414, 9175624264, 19442250125, 40851448761, 85157787033, 176200110937

Offset: 1

N. J. A. Sloane, Mira Bernstein

nonn

George E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 190.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100; alternative link.
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]

Cf. A000334, A000335.

Cf. A007326, A007328, A007329, A007330, A008780, A042984.

a(n) = A000335(n) - A000334(n). - Sean A. Irvine, Dec 18 2017

a(11)-a(23) from Sean A. Irvine, Dec 18 2017

More terms from Amiram Eldar, May 11 2024

A007329 Unexplained difference between two partition generating functions.

Original entry on oeis.org

0, 0, 0, 0, 0, 35, 210, 1001, 3927, 13971, 46592, 148337, 455609, 1362656, 3989914, 11504669, 32804967, 92877609, 261846522

Offset: 1

N. J. A. Sloane, Mira Bernstein

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100.
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]

Cf. A000416, A000417.

Cf. A007326, A007327, A007328, A007330.

a(n) = A000417(n) - A000416(n). - Sean A. Irvine, Dec 18 2017

a(11)-a(19) from Sean A. Irvine, Dec 18 2017

A007330 Difference between the number of 7-dimensional partitions of n and an approximation derived from binomial(n,6).

Original entry on oeis.org

0, 0, 0, 0, 0, 70, 490, 2632, 11606, 46375, 173362, 618086, 2123709, 7086864, 23085942, 73761644, 232002909, 720819622, 2218608551, 6782480955

Offset: 1

N. J. A. Sloane, Mira Bernstein

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100; alternative link.
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]

Cf. A000427, A000428, A007326, A007327, A007328, A007329.

a(n) = A000428(n) - A000427(n). - Sean A. Irvine, Dec 18 2017

a(11)-a(18) from Sean A. Irvine, Dec 18 2017

a(19)-a(20) from Amiram Eldar, May 11 2024

cp's OEIS Frontend

A007326 Difference between A000294 and the number of solid partitions of n (A000293).

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A007327 Difference between two partition g.f.s.

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A007329 Unexplained difference between two partition generating functions.

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A007330 Difference between the number of 7-dimensional partitions of n and an approximation derived from binomial(n,6).

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