A261800 Number of 8-compositions of n: matrices with 8 rows of nonnegative integers with positive column sums and total element sum n.

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

Alois P. Heinz, Table of n, a(n) for n = 0..925

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).

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 A234513

Adjacent sequences: A261797 A261798 A261799 * A261801 A261802 A261803

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 01 2015

Status

approved