%I #10 Mar 03 2019 12:30:44
%S 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,
%T 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,
%U -9,1,-19,1,-9,1
%N 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(.).
%C Row sums are 1, 2, 1, 6, -7, 10, 1, 20, -27, 16, -59, ...
%e Rows n >= 0, 0 <= k <= n begin
%e 1;
%e 1, 1;
%e 1, -1, 1;
%e 1, 2, 2, 1;
%e 1, -5, 1, -5, 1;
%e 1, 3, 1, 1, 3, 1;
%e 1, -2, 4, -5, 4, -2, 1;
%e 1, 3, 3, 3, 3, 3, 3, 1;
%e 1, -11, 1, -7, 5, -7, 1, -11, 1;
%e 1, 4, -2, 1, 4, 4, 1, -2, 4, 1;
%e 1, -9, 1, -19, 1, -9, 1, -19, 1, -9, 1;
%p 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:
%p A178304 := proc(n,m) 1 + A002487(n+1)*( A002487(m+1)+A002487(n-m+1)-1-A002487(n+1) ) ; end proc:
%p seq(seq(A178304(n,k),k=0..n),n=0..15) ; # _N. J. A. Sloane_, Jul 20 2010
%t a[0] = 0; a[1] = 1;
%t a[n_] := a[n] = If[Mod[n, 2] == 0, a[Floor[n/2]], a[ Floor[(n - 1)/2]] + a[Floor[(n + 1)/2]]];
%t 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]);
%t Table[Table[tg[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%Y Cf. A002487, A177443.
%K sign,tabl,easy
%O 0,8
%A _Roger L. Bagula_ and _Gary W. Adamson_, May 24 2010
%E Definition simplified by the Assoc. Eds. of the OEIS, Jul 20 2010
|