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URL: https://oeis.org/A261800

⇱ A261800 - OEIS

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A261800
Number of 8-compositions of n: matrices with 8 rows of nonnegative integers with positive column sums and total element sum n.
2
1, 8, 100, 1208, 14554, 175352, 2112772, 25456328, 306717703, 3695574048, 44527157584, 536497912672, 6464145163032, 77885061063584, 938419943222768, 11306815168562400, 136233325153964242, 1641445323534504928, 19777413104380161776, 238293693669343744032
OFFSET
0,2
COMMENTS
Also the number of compositions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order.
LINKS
Index entries for linear recurrences with constant coefficients, signature (16,-56,112,-140,112,-56,16,-2).
FORMULA
G.f.: (1-x)^8/(2*(1-x)^8-1).
a(n) = A261780(n,8).
a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+8*k,n). - Seiichi Manyama, Aug 06 2024
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(j+7, 7), j=1..n))
end:
seq(a(n), n=0..20);
MATHEMATICA
CoefficientList[Series[(1-x)^8/(2(1-x)^8-1), {x, 0, 30}], x] (* or *) LinearRecurrence[{16, -56, 112, -140, 112, -56, 16, -2}, {1, 8, 100, 1208, 14554, 175352, 2112772, 25456328, 306717703}, 30] (* Harvey P. Dale, Jul 15 2023 *)
CROSSREFS
Column k=8 of A261780.
Sequence in context: A229282 A179485 A144072 * A208705 A246237 A390386
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 01 2015
STATUS
approved