A346229
Number of n-step 8-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
Original entry on oeis.org
1, 1, 9, 73, 545, 3881, 27761, 208593, 1655241, 13490897, 110135641, 895031361, 7279880713, 59647817713, 493774294393, 4125976137817, 34688652854097, 292496479087385, 2469649871976929, 20883345481893257, 177031405058676369, 1505681846157691769
Offset: 0
-
b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
end:
a:= n-> b(n, [0$8]):
seq(a(n), n=0..27);
A346230
Number of n-step 9-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
Original entry on oeis.org
1, 1, 10, 91, 766, 6130, 48628, 399403, 3459646, 31119382, 283230172, 2571653926, 23283756892, 211338730900, 1932349078216, 17832773405035, 165944764694782, 1552985405704558, 14576920303430476, 137021547292573186, 1289614077968369716, 12160967374482417964
Offset: 0
-
b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
end:
a:= n-> b(n, [0$9]):
seq(a(n), n=0..27);
A346231
Number of n-step 10-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
Original entry on oeis.org
1, 1, 11, 111, 1041, 9271, 81101, 725021, 6794611, 66508821, 665254791, 6674936601, 66755513931, 666897563121, 6686651885691, 67529142206631, 687755702224881, 7056692549851951, 72780288870993221, 752810967999798491, 7798329264904129201, 80874531810513679011
Offset: 0
-
b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
end:
a:= n-> b(n, [0$10]):
seq(a(n), n=0..27);