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%I A109056 #13 Apr 01 2024 13:08:00
%S A109056 1,1,4,58,3236,713727,627642640,2205897096672,31004442653082720,
%T A109056 1743005531132374350208,391947224244531572312436328,
%U A109056 352545281714327012273215572739472,1268416358395092955994185170741834144224,18254446075150458724007419019753847268167282688
%N A109056 To compute a(n) we first write down 4^n 1's in a row. Each row takes the rightmost 4th 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 4th part. The single element in the last row is a(n).
%H A109056 Alois P. Heinz, <a href="/A109056/b109056.txt">Table of n, a(n) for n = 0..58</a>
%e A109056 For example, for n=3 the array looks like this:
%e A109056 1..1.....1..1..1..1..1..1..1..1..1..1..1..1..1..1..1..1..1
%e A109056 ............1..2..3..4..5..6..7..8..9.10.11.12.13.14.15.16
%e A109056 ...............................................13.27.42.58
%e A109056 ........................................................58
%e A109056 Therefore a(4)=58.
%p A109056 proc(n::nonnegint) local f,a; if n=0 or n=1 then return 1; end if; f:=L->[seq(add(L[i],i=3*nops(L)/4+1..j),j=3*nops(L)/4+1..nops(L))]; a:=f([seq(1,j=1..4^n)]); while nops(a)>4 do a:=f(a) end do; a[4]; end proc;
%t A109056 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 A109056 a[n_] := A[n, 4];
%t A109056 Table[a[n], {n, 0, 13}] (* _Jean-François Alcover_, Apr 01 2024, after _Alois P. Heinz_ in A355576 *)
%Y A109056 Cf. A107354, A109055, A109057, A109058, A109059, A109060, A109061.
%Y A109056 Column k=4 of A355576.
%K A109056 nonn
%O A109056 0,3
%A A109056 _Augustine O. Munagi_, Jun 17 2005
%E A109056 More terms from _Alois P. Heinz_, Jul 06 2022

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