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%I #7 Jul 12 2021 21:46:37
%S 1,1,8,57,372,2332,14960,102173,732124,5306652,38253888,275352960,
%T 1996376544,14642264736,108536296800,809764874325,6057499056204,
%U 45368515203628,340472040666080,2563725956556584,19381407270110656,147036877912623840,1118355187220657856
%N Number of n-step 7-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
%H Alois P. Heinz, <a href="/A346228/b346228.txt">Table of n, a(n) for n = 0..90</a>
%F a(n) == 1 (mod 7).
%p b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
%p add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
%p i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
%p end:
%p a:= n-> b(n, [0$7]):
%p seq(a(n), n=0..27);
%Y Column k=7 of A335570.
%K nonn,walk
%O 0,3
%A _Alois P. Heinz_, Jul 11 2021