A005406 Number of protruded partitions of n with largest part at most 5. (Formerly M2569)

1, 3, 6, 13, 25, 49, 91, 170, 309, 558, 992, 1752, 3062, 5317, 9166, 15712, 26784, 45447, 76775, 129203, 216662, 362177, 603671, 1003566, 1664389, 2754382, 4549207, 7500096, 12344840, 20288723, 33298979, 54584077, 89373081, 146182754

Offset

1,2

References

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

R. P. Stanley, Ordered structures and partitions, Memoirs of the Amer. Math. Soc., no. 119 (1972).

Links

Table of n, a(n) for n=1..34.

R. P. Stanley, A Fibonacci lattice, Fib. Quart., 13 (1975), 215-232.

Formula

G.f.: (1-x)^5/Product(1-x-x^i+x^(1+2*i), i=1..5)-1. - Emeric Deutsch, Dec 19 2004

Maple

G:=(1-x)^5/Product(1-x-x^i+x^(1+2*i), i=1..5)-1: Gser:=series(G, x=0, 39): seq(coeff(Gser, x^n), n=1..37); # Emeric Deutsch, Dec 19 2004

Mathematica

Rest@ CoefficientList[Series[(1 - x)^5/Product[1 - x - x^i + x^(1 + 2 i), {i, 5}] - 1, {x, 0, 34}], x] (* Michael De Vlieger, Sep 05 2017 *)

Crossrefs

Sequence in context: A182808 A285461 A324129 * A005407 A005116 A121349

Adjacent sequences: A005403 A005404 A005405 * A005407 A005408 A005409

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Emeric Deutsch, Dec 19 2004

Status

approved