A178304 Triangle T(n,m) = 1 + f(n+1)*(f(m+1) + f(n-m+1) - 1 - f(n+1)), read by rows, where f(.)=A002487(.).
1, 1, 1, 1, -1, 1, 1, 2, 2, 1, 1, -5, 1, -5, 1, 1, 3, 1, 1, 3, 1, 1, -2, 4, -5, 4, -2, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, -11, 1, -7, 5, -7, 1, -11, 1, 1, 4, -2, 1, 4, 4, 1, -2, 4, 1, 1, -9, 1, -19, 1, -9, 1, -19, 1, -9, 1
Offset: 0
Examples
Rows n >= 0, 0 <= k <= n begin 1; 1, 1; 1, -1, 1; 1, 2, 2, 1; 1, -5, 1, -5, 1; 1, 3, 1, 1, 3, 1; 1, -2, 4, -5, 4, -2, 1; 1, 3, 3, 3, 3, 3, 3, 1; 1, -11, 1, -7, 5, -7, 1, -11, 1; 1, 4, -2, 1, 4, 4, 1, -2, 4, 1; 1, -9, 1, -19, 1, -9, 1, -19, 1, -9, 1;
Programs
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Maple
A002487 := proc(n) option remember; if n <=1 then n; else if type(n,'even') then procname(n/2) ; else procname((n-1)/2)+procname(1+(n-1)/2) ; end if; end if; end proc: A178304 := proc(n,m) 1 + A002487(n+1)*( A002487(m+1)+A002487(n-m+1)-1-A002487(n+1) ) ; end proc: seq(seq(A178304(n,k),k=0..n),n=0..15) ; # N. J. A. Sloane, Jul 20 2010
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Mathematica
a[0] = 0; a[1] = 1; a[n_] := a[n] = If[Mod[n, 2] == 0, a[Floor[n/2]], a[ Floor[(n - 1)/2]] + a[Floor[(n + 1)/2]]]; tg[n_, m_] := 1 + a[n + 1]*a[m + 1] + a[n + 1]*a[n - m + 1] - (a[n + 1]*a[ 0 + 1] + a[n + 1]*a[n - 0 + 1]); Table[Table[tg[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
Extensions
Definition simplified by the Assoc. Eds. of the OEIS, Jul 20 2010
Comments