A109058 To compute a(n) we first write down 6^n 1's in a row. Each row takes the rightmost 6th 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 6th part. The single element in the last row is a(n).

1, 1, 6, 201, 39656, 46769781, 330736663032, 14031372754200653, 3571582237574150514024, 5454701025672508908169570740, 49984143782624329482858175943128416, 2748177454593265010973723857947479180947553, 906585004703475512437226615670665677815744239819376

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..51

Example

For example, for n=3 the array, from 2nd row, follows:
1..2..3.....25..26..27..28..29..30..31..32..33..34..35..36
....................................31..63..96.130.165.201
.......................................................201
Therefore a(3)=201.

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=5*nops(L)/6+1..j), j=5*nops(L)/6+1..nops(L))]; a:=f([seq(1, j=1..6^n)]); while nops(a)>6 do a:=f(a) end do; a[6]; 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, 6];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Apr 01 2024, after Alois P. Heinz in A355576 *)

Crossrefs

Cf. A107354, A109055, A109056, A109057, A109059, A109060, A109061, A109062.

Column k=6 of A355576.

Sequence in context: A340557 A305167 A112845 * A274481 A256799 A003743

Adjacent sequences: A109055 A109056 A109057 * A109059 A109060 A109061

Keyword

nonn

Author

Augustine O. Munagi, Jun 17 2005

Extensions

More terms from Alois P. Heinz, Jul 06 2022

Status

approved