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A005407
Number of protruded partitions of n with largest part at most 6.
(Formerly M2570)
1
1, 3, 6, 13, 25, 50, 93, 175, 320, 582, 1041, 1851, 3253, 5682, 9848, 16970, 29070, 49559, 84090, 142107, 239239, 401404, 671386, 1119799, 1862861, 3091708, 5120090, 8462535, 13961695, 22996307, 37819865, 62112581, 101879568, 166912537, 273166466, 446623176
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
R. P. Stanley, A Fibonacci lattice, Fib. Quart., 13 (1975), 215-232.
FORMULA
G.f.: (1-x)^6/Product_{i=1..6} (1-x-x^i+x^(1+2*i)) - 1. - Emeric Deutsch, Dec 19 2004
MAPLE
G:=(1-x)^6/Product(1-x-x^i+x^(1+2*i), i=1..6)-1: Gser:=series(G, x=0, 39): seq(coeff(Gser, x^n), n=1..37); # Emeric Deutsch, Dec 19 2004
MATHEMATICA
CoefficientList[Series[(1-x)^6/Product[1-x-x^i+x^(1+2i), {i, 6}]-1, {x, 0, 40}], x] (* Harvey P. Dale, Jan 23 2015 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( -1 + (1-x)^6/(&*[1-x-x^j+x^(2*j+1): j in [1..6]]) )); // G. C. Greubel, Nov 19 2022
(SageMath)
def A005407_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( -1 + (1-x)^6/product(1-x-x^j+x^(2*j+1) for j in (1..6)) ).list()
a=A005407_list(50); a[1:] # G. C. Greubel, Nov 19 2022
CROSSREFS
Sequence in context: A285461 A324129 A005406 * A005116 A121349 A215984
KEYWORD
nonn
EXTENSIONS
More terms from Emeric Deutsch, Dec 19 2004
STATUS
approved