A005404 Number of protruded partitions of n with largest part at most 3. (Formerly M2555)

1, 3, 6, 12, 22, 42, 75, 135, 238, 416, 719, 1236, 2107, 3574, 6030, 10130, 16950, 28267, 46993, 77916, 128874, 212701, 350375, 576165, 945984, 1551009, 2539790, 4154212, 6787891, 11081022, 18074324, 29458899, 47981563, 78102314, 127060462

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: (1-x)^3/Product(1-x-x^i+x^(1+2*i), i=1..3)-1. - Emeric Deutsch, Dec 19 2004

Maple

G:=(1-x)^3/Product(1-x-x^i+x^(1+2*i), i=1..3)-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)^3/Product[1 - x - x^i + x^(1 + 2 i), {i, 3}] - 1, {x, 0, 35}], x] (* Michael De Vlieger, Sep 05 2017 *)

Crossrefs

Sequence in context: A236913 A288348 A018078 * A249795 A097939 A249565

Adjacent sequences: A005401 A005402 A005403 * A005405 A005406 A005407

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Emeric Deutsch, Dec 19 2004

Status

approved