This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195662 #26 Nov 27 2012 10:23:38
%S A195662 -3,2,0,2,0,3,2,0,1,0,2,0,-1,0,-3,2,0,-3,0,-4,0,2,0,-5,0,-3,0,3,2,0,
%T A195662 -7,0,0,0,7,0,2,0,-9,0,5,0,10,0,-3,2,0,-11,0,12,0,10,0,-10,0,2,0,-13,
%U A195662 0,21,0,5,0,-20,0,3,2,0,-15,0,32,0,-7,0,-30,0,13,0
%N A195662 Triangle T(n,k) read by rows: T(0,0)= -3, T(1,0)= 2, T(1,1) = 0 and T(n,k) = T(n-1,k) -T(n-2,k-2) otherwise.
%C A195662 In the notation of A195673, this defines polynomials P(n,x,p=-3,q=2), where p and q are the values of the constant and linear order for n=0 and 1.
%C A195662 Row sums -- the value P(n,1,-3,2) of the polynomial -- are A130848(n+5).
%C A195662 For general seed values in the two top rows of the triangle, the recurrence T(n,k) = T(n-1,k) - T(n-2,k-2) defines the triangle
%C A195662 p;
%C A195662 q, 0;
%C A195662 q, 0, -p;
%C A195662 q, 0, -p-q, 0;
%C A195662 q, 0, -p-2q, 0, p;
%C A195662 q, 0, -p-3q, 0, 2p+q, 0;
%C A195662 and a companion triangle by adding 1 to both seed values:
%C A195662 p+1;
%C A195662 q+1, 0;
%C A195662 q+1, 0, -p-1;
%C A195662 q+1, 0, -p-q-2, 0;
%C A195662 q+1, 0, -p-2q-3, 0, p+1;
%C A195662 q+1, 0, -p-3q-4, 0, 2p+q+3, 0;
%C A195662 The point-by-point difference between two companions is P(n,x,p+1,q+1) - P(n,x,p,q) = S(n,x) as represented (with increasing exponents) by A053119.
%C A195662 Examples of such triangles are A053119 (p=q=1), A192575 (p=1, q=2),
%C A195662 A162514 (p=2, q=1, up to a sign factor), A192011 (p=-1, q=2), A135929 (p=-2, q=1, apart from a irregular leading T(0,0)).
%F A195662 T(n,0) = 2 (n>0).
%F A195662 T(n,2) = -A060747(n-3), n>2.
%F A195662 T(n,4) = A028347(n-5), n>6.
%F A195662 T(2n,2n) = -3*(-1)^n ; T(n, 2k-1) = 0 ; T(2n+1,2n) = -(3n-2)*(-1)^n. - M. F. Hasler, Sep 28 2011
%e A195662 The first few rows are
%e A195662 -3;
%e A195662 2, 0;
%e A195662 2, 0, 3;
%e A195662 2, 0, 1, 0;
%e A195662 2, 0, -1, 0, -3;
%e A195662 2, 0, -3, 0, -4, 0;
%e A195662 2, 0, -5, 0, -3, 0, 3;
%e A195662 2, 0, -7, 0, 0, 0, 7, 0;
%e A195662 2, 0, -9, 0, 5, 0, 10, 0, -3;
%e A195662 2, 0, -11, 0, 12, 0, 10, 0, -10, 0;
%e A195662 2, 0, -13, 0, 21, 0, 5, 0, -20, 0, 3;
%t A195662 p = -3; q = 2; t[0, 0] = p; t[_, 0] = q; t[_, _?OddQ] = 0; t[n_, k_] /; k > n = 0; t[n_ /; n >= 0, k_ /; k >= 0] := t[n, k] = t[n-1, k] - t[n-2, k-2]; Table[t[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Nov 27 2012 *)
%Y A195662 Cf. A135929, A192011.
%K A195662 sign,tabl,easy
%O A195662 0,1
%A A195662 _Paul Curtz_, Sep 22 2011