A109061 To compute a(n) we first write down 9^n 1's in a row. Each row takes the rightmost 9th part of the previous row and each element in it equals sum of the elements of the previous row starting with the first of the rightmost 9th part. The single element in the last row is a(n).

1, 1, 9, 693, 476121, 2940705927, 163444130390781, 81756588582353417271, 368059416198072536171078649, 14912674110246473369128526689667934, 5437955149300119215042866669813503145575607, 17846712348533391270843269203829434120473501691723788

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..46

Example

For example, for n=3 the array, from 2nd row, follows:
1..2..3.....70..71..72..73..74..75..76..77..78..79..80..81
........................73.147.222.298.375.453.532.612.693
.......................................................693
Therefore a(3)=693.

Maple

proc(n::nonnegint) local f, a; if n=0 or n=1 then return 1; end if; f:=L->[seq(add(L[i], i=8*nops(L)/9+1..j), j=8*nops(L)/9+1..nops(L))]; a:=f([seq(1, j=1..9^n)]); while nops(a)>9 do a:=f(a) end do; a[9]; end proc;

Mathematica

A[n_, k_] := A[n, k] = If[n == 0, 1, -Sum[A[j, k]*(-1)^(n - j)* Binomial[If[j == 0, 1, k^j], n - j], {j, 0, n - 1}]];
a[n_] := A[n, 9];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Apr 01 2024, after Alois P. Heinz in A355576 *)

Crossrefs

Cf. A107354, A109055, A109056, A109057, A109058, A109059, A109060, A109062.

Column k=9 of A355576.

Sequence in context: A053973 A059492 A322488 * A332169 A282181 A053515

Adjacent sequences: A109058 A109059 A109060 * A109062 A109063 A109064

Keyword

nonn

Author

Augustine O. Munagi, Jun 17 2005

Extensions

More terms from Alois P. Heinz, Jul 06 2022

Status

approved