A136745 - OEIS

%I #11 Jul 26 2021 15:45:48

%S 1,-1,0,1,-1,0,-1,0,1,1,0,-2,0,-1,0,1,1,0,2,0,-3,0,-1,0,1,-1,0,3,0,3,

%T 0,-4,0,-1,0,1,-1,0,-3,0,6,0,4,0,-5,0,-1,0,1,1,0,-4,0,-6,0,10,0,5,0,

%U -6,0,-1,0,1,1,0,4,0,-10,0,-10,0,15,0,6,0,-7,0,-1,0,1,-1,0,5,0,10,0,-20,0,-15,0,21,0,7,0,-8,0,-1,0,1,-1,0,-5,0,15,0,20,0

%N Irregular triangle T(0,0)=1, T(1,0)=-1, T(1,1)=0, T(1,2)=1 and T(n,k) = T(n-1,k-2)-T(n-2,k).

%C Row sums are probably a repeating sequence 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0,...

%C This is simply A130777 with columns of zeros inserted in odd-numbered columns. - _R. J. Mathar_, Nov 04 2011

%e 1;

%e -1, 0, 1;

%e -1, 0, -1, 0, 1;

%e 1, 0, -2, 0, -1, 0, 1;

%e 1, 0, 2, 0, -3, 0, -1, 0, 1;

%e -1, 0, 3, 0, 3, 0, -4, 0, -1, 0, 1;

%e -1, 0, -3, 0, 6, 0, 4, 0, -5, 0, -1, 0, 1;

%e 1, 0, -4, 0, -6, 0, 10, 0, 5, 0, -6, 0, -1, 0,1;

%e 1, 0, 4,0, -10, 0, -10, 0, 15, 0, 6, 0, -7, 0, -1, 0, 1;

%e -1, 0, 5, 0, 10, 0, -20, 0, -15, 0, 21, 0, 7, 0, -8, 0, -1, 0, 1;

%e -1, 0, -5, 0, 15, 0,20, 0, -35, 0, -21, 0, 28, 0, 8, 0, -9, 0, -1, 0, 1;

%t Clear[p, x, n] p[x, 0] = 1; p[x, 1] = x^2 - 1; p[x_, n_] := p[x, n] = x^2*p[x, n - 1] - p[x, n - 2]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}];

%Y Cf. A130777.

%K easy,tabf,sign

%O 0,12

%A _Roger L. Bagula_, Mar 19 2008