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).
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 01 2015
STATUS
approved