cp's OEIS Frontend

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).

%I A109058 #11 Apr 01 2024 13:38:44
%S A109058 1,1,6,201,39656,46769781,330736663032,14031372754200653,
%T A109058 3571582237574150514024,5454701025672508908169570740,
%U A109058 49984143782624329482858175943128416,2748177454593265010973723857947479180947553,906585004703475512437226615670665677815744239819376
%N 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).
%H A109058 Alois P. Heinz, <a href="/A109058/b109058.txt">Table of n, a(n) for n = 0..51</a>
%e A109058 For example, for n=3 the array, from 2nd row, follows:
%e A109058 1..2..3.....25..26..27..28..29..30..31..32..33..34..35..36
%e A109058 ....................................31..63..96.130.165.201
%e A109058 .......................................................201
%e A109058 Therefore a(3)=201.
%p A109058 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;
%t A109058 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}]];
%t A109058 a[n_] := A[n, 6];
%t A109058 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Apr 01 2024, after _Alois P. Heinz_ in A355576 *)
%Y A109058 Cf. A107354, A109055, A109056, A109057, A109059, A109060, A109061, A109062.
%Y A109058 Column k=6 of A355576.
%K A109058 nonn
%O A109058 0,3
%A A109058 _Augustine O. Munagi_, Jun 17 2005
%E A109058 More terms from _Alois P. Heinz_, Jul 06 2022