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A123975 Number of Garden of Eden partitions of n in Bulgarian Solitaire. 3
0, 0, 1, 1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 86, 113, 147, 190, 243, 311, 394, 499, 627, 786, 980, 1220, 1510, 1865, 2294, 2816, 3443, 4202, 5110, 6203, 7507, 9067, 10923, 13135, 15755, 18865, 22540, 26885, 32001, 38032, 45112, 53430, 63171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) gives the number of times n occurs in A225794. - Antti Karttunen, Jul 27 2013

LINKS

Table of n, a(n) for n=1..48.

Brian Hopkins and Michael A. Jones, Shift-induced dynamical systems on partitions and compositions.

Brian Hopkins and James A. Sellers, Exact enumeration of Garden of Eden partitions.

FORMULA

a(n) = A064173(n)-A101198(n).

MAPLE

p:=product(1/(1-q^i), i=1..200)*sum((-1)^(r-1)*q^((3*r^2+3*r)/2), r=1..200):s:=series(p, q, 200): for j from 0 to 199 do printf(`%d, `, coeff(s, q, j)) od: - James A. Sellers, Nov 30 2006

CROSSREFS

Cf. A227753, A225794, A226062.

Sequence in context: A104503 A027340 A000701 * A214077 A094984 A107332

Adjacent sequences:  A123972 A123973 A123974 * A123976 A123977 A123978

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Nov 23 2006

EXTENSIONS

More terms from James A. Sellers, Nov 30 2006

STATUS

approved

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Last modified May 23 08:43 EDT 2017. Contains 286909 sequences.