A003292 Number of 4-line partitions of n decreasing across rows. (Formerly M1050)

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

1,2

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.

Formula

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A024622 A034337 A083024 * A007864 A277271 A394628

Adjacent sequences: A003289 A003290 A003291 * A003293 A003294 A003295

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Joerg Arndt, Oct 12 2017

Status

approved