cp's OEIS Frontend

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

%I A261800 #16 Aug 06 2024 09:56:33
%S A261800 1,8,100,1208,14554,175352,2112772,25456328,306717703,3695574048,
%T A261800 44527157584,536497912672,6464145163032,77885061063584,
%U A261800 938419943222768,11306815168562400,136233325153964242,1641445323534504928,19777413104380161776,238293693669343744032
%N A261800 Number of 8-compositions of n: matrices with 8 rows of nonnegative integers with positive column sums and total element sum n.
%C A261800 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.
%H A261800 Alois P. Heinz, <a href="/A261800/b261800.txt">Table of n, a(n) for n = 0..925</a>
%H A261800 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (16,-56,112,-140,112,-56,16,-2).
%F A261800 G.f.: (1-x)^8/(2*(1-x)^8-1).
%F A261800 a(n) = A261780(n,8).
%F A261800 a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+8*k,n). - _Seiichi Manyama_, Aug 06 2024
%p A261800 a:= proc(n) option remember; `if`(n=0, 1,
%p A261800       add(a(n-j)*binomial(j+7, 7), j=1..n))
%p A261800     end:
%p A261800 seq(a(n), n=0..20);
%t A261800 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 *)
%Y A261800 Column k=8 of A261780.
%K A261800 nonn,easy
%O A261800 0,2
%A A261800 _Alois P. Heinz_, Sep 01 2015