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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(.).

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