A005404 - OEIS

%I M2555 #19 Sep 06 2017 02:47:08

%S 1,3,6,12,22,42,75,135,238,416,719,1236,2107,3574,6030,10130,16950,

%T 28267,46993,77916,128874,212701,350375,576165,945984,1551009,2539790,

%U 4154212,6787891,11081022,18074324,29458899,47981563,78102314,127060462

%N Number of protruded partitions of n with largest part at most 3.

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

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

%H Vincenzo Librandi, <a href="/A005404/b005404.txt">Table of n, a(n) for n = 1..1000</a>

%H R. P. Stanley, <a href="http://www.fq.math.ca/Scanned/13-3/stanley.pdf">A Fibonacci lattice</a>, Fib. Quart., 13 (1975), 215-232.

%F G.f.: (1-x)^3/Product(1-x-x^i+x^(1+2*i), i=1..3)-1. - _Emeric Deutsch_, Dec 19 2004

%p 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

%t 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 *)

%K nonn

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from _Emeric Deutsch_, Dec 19 2004