A005403 - OEIS

A005403

Number of protruded partitions of n with largest part at most 2.
(Formerly M2463)

1, 3, 5, 10, 17, 31, 53, 92, 156, 265, 445, 746, 1243, 2066, 3421, 5652, 9314, 15320, 25152, 41232, 67497, 110361, 180249, 294115, 479500, 781143, 1271675, 2068987, 3364358, 5468074, 8883329, 14425997, 23418648, 38004865, 61658326, 100007327

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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..36.

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

FORMULA

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

MAPLE

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

CROSSREFS

Sequence in context: A192757 A079934 A215004 * A018072 A090170 A301751

Adjacent sequences: A005400 A005401 A005402 * A005404 A005405 A005406

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Emeric Deutsch, Dec 19 2004

STATUS

approved