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A259875 Irregular triangle read by rows: coefficients (highest degree first) of polynomials defined by p_0(x)=0, p_1(x)=p_2(x)=1, p_3(x)=x+1; p_n(x)=x*p_{n-2}(x)-p_{n-4}(x).

%I A259875 #22 Jun 12 2018 08:19:40
%S A259875 0,1,1,1,1,1,0,1,1,-1,1,0,-1,1,1,-2,-1,1,0,-2,0,1,1,-3,-2,1,1,0,-3,0,
%T A259875 1,1,1,-4,-3,3,1,1,0,-4,0,3,0,1,1,-5,-4,6,3,-1,1,0,-5,0,6,0,-1,1,1,-6,
%U A259875 -5,10,6,-4,-1,1,0,-6,0,10,0,-4,0,1,1,-7,-6,15,10,-10,-4,1
%N A259875 Irregular triangle read by rows: coefficients (highest degree first) of polynomials defined by p_0(x)=0, p_1(x)=p_2(x)=1, p_3(x)=x+1; p_n(x)=x*p_{n-2}(x)-p_{n-4}(x).
%H A259875 Alois P. Heinz, <a href="/A259875/b259875.txt">Rows n = 0..200, flattened</a>
%H A259875 A. F. Horadam, R. P. Loh and A. G. Shannon, <a href="/A005013/a005013.pdf">Divisibility properties of some Fibonacci-type sequences</a>, pp. 55-64 of Combinatorial Mathematics VI (Armidale 1978), Lect. Notes Math. 748, 1979. [Annotated scanned copy]
%H A259875 A. F. Horadam, R. P. Loh and A. G. Shannon, <a href="https://doi.org/10.1007/BFb0102684">Divisibility properties of some Fibonacci-type sequences</a>, pp. 55-64 of Combinatorial Mathematics VI (Armidale 1978), Lect. Notes Math. 748, 1979.
%e A259875 Triangle begins:
%e A259875 0;
%e A259875 1;
%e A259875 1;
%e A259875 1, 1;
%e A259875 1, 0;
%e A259875 1, 1, -1;
%e A259875 1, 0, -1;
%e A259875 1, 1, -2, -1;
%e A259875 1, 0, -2,  0;
%e A259875 1, 1, -3, -2, 1;
%e A259875 1, 0, -3,  0, 1;
%e A259875 1, 1, -4, -3, 3, 1;
%e A259875 1, 0, -4,  0, 3, 0;
%e A259875 ...
%p A259875 p:= proc(n) option remember; expand(`if`(n=0, 0,
%p A259875      `if`(n<3, 1, `if`(n=3, x+1, x*p(n-2)-p(n-4)))))
%p A259875     end:
%p A259875 T:= n-> `if`(n=0, 0, (s-> seq(coeff(s, x, degree(s)-i)
%p A259875         , i=0..degree(s)))(p(n))):
%p A259875 seq(T(n), n=0..20);  # _Alois P. Heinz_, Jul 10 2015
%t A259875 p[0] = 0&; p[1] = p[2] = 1&; p[3] = #+1&; p[n_][x_] := p[n, x] = x*p[n-2][x] - p[n-4][x];
%t A259875 row[0] = {0}; row[n_] := CoefficientList[p[n][x], x] // Reverse;
%t A259875 Table[row[n], {n, 0, 20}] // Flatten (* _Jean-François Alcover_, Jun 12 2018 *)
%Y A259875 p_n(3) gives A005013.
%K A259875 sign,tabf,look
%O A259875 0,16
%A A259875 _N. J. A. Sloane_, Jul 09 2015
%E A259875 More terms from _Alois P. Heinz_, Jul 10 2015