A005405 Number of protruded partitions of n with largest part at most 4. (Formerly M2565)

1, 3, 6, 13, 24, 47, 86, 159, 285, 509, 895, 1565, 2708, 4660, 7964, 13543, 22912, 38604, 64785, 108356, 180661, 300384, 498183, 824365, 1361302, 2243799, 3692159, 6066161, 9952786, 16309055, 26694132, 43646685, 71297770, 116366274, 189774755, 309271954, 503687536

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)^4/Product(1-x-x^i+x^(1+2*i), i=1..4)-1. - Emeric Deutsch, Dec 19 2004

Maple

G:=(1-x)^4/Product(1-x-x^i+x^(1+2*i), i=1..4)-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)^4/Product[1 - x - x^i + x^(1 + 2 i), {i, 4}] - 1, {x, 0, 34}], x] (* Michael De Vlieger, Sep 05 2017 *)

Crossrefs

Sequence in context: A293421 A018081 A001452 * A225196 A301597 A225197

Adjacent sequences: A005402 A005403 A005404 * A005406 A005407 A005408

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Emeric Deutsch, Dec 19 2004

Status

approved