cp's OEIS Frontend

A109059 To compute a(n) we first write down 7^n 1's in a row. Each row takes the rightmost 7th 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 7th part. The single element in the last row is a(n).

%I A109059 #11 Apr 01 2024 13:38:58
%S A109059 1,1,7,322,102249,226742516,3518406903403,382149784071841422,
%T A109059 290546585470549214822793,1546306129153609960601346281449,
%U A109059 57606719909341067627899562630623352149,15022729501707009545842655841005666468590455864,27423481304702360472157221630747597794702587610760693525
%N A109059 To compute a(n) we first write down 7^n 1's in a row. Each row takes the rightmost 7th 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 7th part. The single element in the last row is a(n).
%H A109059 Alois P. Heinz, <a href="/A109059/b109059.txt">Table of n, a(n) for n = 0..49</a>
%e A109059 For example, for n=3 the array, from 2nd row, follows:
%e A109059 1..2..3.....38..39..40..41..42..43..44..45..46..47..48..49
%e A109059 ................................43..87.132.178.225.273.322
%e A109059 .......................................................322
%e A109059 Therefore a(3)=322.
%p A109059 proc(n::nonnegint) local f,a; if n=0 or n=1 then return 1; end if; f:=L->[seq(add(L[i],i=6*nops(L)/7+1..j),j=6*nops(L)/7+1..nops(L))]; a:=f([seq(1,j=1..7^n)]); while nops(a)>7 do a:=f(a) end do; a[7]; end proc;
%t A109059 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 A109059 a[n_] := A[n, 7];
%t A109059 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Apr 01 2024, after_Alois P. Heinz_ in A355576 *)
%Y A109059 Cf. A107354, A109055, A109056, A109057, A109058, A109060, A109061, A109062.
%Y A109059 Column k=7 of A355576.
%K A109059 nonn
%O A109059 0,3
%A A109059 _Augustine O. Munagi_, Jun 17 2005
%E A109059 More terms from _Alois P. Heinz_, Jul 06 2022