A003292 Number of 4-line partitions of n decreasing across rows.

1, 2, 4, 7, 11, 19, 29, 46, 70, 106, 156, 232, 334, 482, 686, 971, 1357, 1894, 2612, 3592, 4900, 6656, 8980, 12077, 16137, 21490, 28476, 37600, 49422, 64763, 84511, 109953, 142539, 184244, 237368, 304996, 390688, 499189, 636059, 808489, 1025017, 1296595, 1636173, 2060246, 2588440, 3245381, 4060519, 5070574

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is the number of unlabeled graphs on n nodes whose connected components are a path or a cycle. - Geoffrey Critzer, Nov 28 2011

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• Herbert S. Wilf, Generatingfunctiontology, Academic Press, 1994, page 106.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• M. S. Cheema and W. E. Conway, Numerical investigation of certain asymptotic results in the theory of partitions, Math. Comp., 26 (1972), 999-1005.

Programs

Mathematica

Rest[p=Product[1/(1 - x^i), {i, 1, 20}]; CoefficientList[Series[p^2 (1 - x) (1 - x^2), {x, 0, 20}], x]] (* Geoffrey Critzer, Nov 28 2011 *) (* adapted by Vincenzo Librandi, Oct 12 2017 *)

PARI

\\ program includes a(0) = 1:
c(n) = 1 + (n>=3);
N = 66;  x = 'x + O('x^N);
Vec( 1 / prod(n=1, N, (1 - x^k)^c(n)) )  \\ Joerg Arndt, Oct 12 2017

Formula

G.f.: Product (1 - x^k)^-{c(k)}; c(k) = 1, 1, 2, 2, 2, 2, ....

Extensions

More terms from Joerg Arndt, Oct 12 2017