A109060 To compute a(n) we first write down 8^n 1's in a row. Each row takes the rightmost 8th 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 8th part. The single element in the last row is a(n).

1, 1, 8, 484, 231736, 886208954, 27106585594040, 6632714300472863716, 12983632019302863224103688, 203325054125533158416534341556735, 25472733809776289439071490656049076425792, 25529963965104465687252347321830255523307055463168

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..47

Example

For example, for n=3 the array, from 2nd row, follows:
1..2..3.....53..54..55..56..57..58..59..60..61..62..63..64
............................57.115.174.234.295.357.420.484
.......................................................484
Therefore a(3)=484.

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=7*nops(L)/8+1..j), j=7*nops(L)/8+1..nops(L))]; a:=f([seq(1, j=1..8^n)]); while nops(a)>8 do a:=f(a) end do; a[8]; 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, 8];
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, A109061, A109062.

Column k=8 of A355576.

Sequence in context: A152495 A197096 A332148 * A259926 A282180 A240398

Adjacent sequences: A109057 A109058 A109059 * A109061 A109062 A109063

Keyword

nonn

Author

Augustine O. Munagi, Jun 17 2005

Extensions

More terms from Alois P. Heinz, Jul 06 2022

Status

approved