The On-Line Encyclopedia of Integer Sequences (OEIS)

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A293372

Number of partitions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all eight letters occur at least once in the partition.
(history; published version)

#8 by Vaclav Kotesovec at Wed Oct 11 06:44:30 EDT 2017

STATUS

editing

approved

#7 by Vaclav Kotesovec at Wed Oct 11 06:44:22 EDT 2017

FORMULA

a(n) ~ c * 8^n, where c = 3.3565128773700137140303140039343582841894554205106317247... - Vaclav Kotesovec, Oct 11 2017

STATUS

approved

editing

#6 by Alois P. Heinz at Sat Oct 07 17:16:00 EDT 2017

STATUS

editing

approved

#5 by Alois P. Heinz at Sat Oct 07 17:15:56 EDT 2017

NAME

Number of partitions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all 8 eight letters occur at least once in the partition.

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))

end:

a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(8):

seq(a(n), n=8..30);

STATUS

approved

editing

#4 by Alois P. Heinz at Sat Oct 07 16:50:02 EDT 2017

STATUS

editing

approved

#3 by Alois P. Heinz at Sat Oct 07 16:49:56 EDT 2017

LINKS

Alois P. Heinz, <a href="/A293372/b293372.txt">Table of n, a(n) for n = 8..1000</a>

#2 by Alois P. Heinz at Sat Oct 07 16:48:31 EDT 2017

NAME

allocated for Alois P. Heinz

Number of partitions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all 8 letters occur at least once in the partition.

DATA

95503, 3641992, 80387608, 1322729896, 18385756520, 225257353792, 2541255024732, 26777904754008, 269047552566188, 2594409873644384, 24281765931659608, 221357827678662984, 1978440640155108276, 17375505823280757968, 150542570789825846856, 1288702165811231618744

OFFSET

8,1

CROSSREFS

Column k=8 of A261719.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Oct 07 2017

STATUS

approved

editing

#1 by Alois P. Heinz at Sat Oct 07 16:09:50 EDT 2017

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved