A261799 Number of 7-compositions of n: matrices with 7 rows of nonnegative integers with positive column sums and total element sum n.

1, 7, 77, 819, 8687, 92141, 977347, 10366833, 109962202, 1166381804, 12371946734, 131230670312, 1391978902090, 14764881252772, 156612803600094, 1661210126351328, 17620647995924820, 186904251828901124, 1982515022137687464, 21028766197355391048

Offset

0,2

Comments

Also the number of compositions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..975

Index entries for linear recurrences with constant coefficients, signature (14,-42,70,-70,42,-14,2).

Formula

G.f.: (1-x)^7/(2*(1-x)^7-1).

a(n) = A261780(n,7).

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-j)*binomial(j+6, 6), j=1..n))
    end:
seq(a(n), n=0..20);

Crossrefs

Column k=7 of A261780.

Sequence in context: A061546 A002281 A097983 * A246236 A349364 A267709

Adjacent sequences: A261796 A261797 A261798 * A261800 A261801 A261802

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 01 2015

Status

approved