%I A102426
%S A102426 0,1,1,1,1,2,1,1,3,1,3,4,1,1,6,5,1,4,10,6,1,1,10,15,7,1,5,20,21,8,1,1,
%T A102426 15,35,28,9,1
%N A102426 Triangle read by rows giving coefficients of polynomials defined by F(0)=0, 
               F(1)=1, F(n+1) = F(n) + x*F(n-1).
%C A102426 F(n) + 2x * F(n-1) gives Lucas polynomials (cf. A034807). - Maxim Krikun 
               (krikun(AT)iecn.u-nancy.fr), Jun 24 2007
%C A102426 Essentially the same as A098925. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 30 2008]
%F A102426 Alternatively, as n is even or odd: T(n-2, k) + T(n-1, k-1) = T(n, k) 
               T(n-2, k) + T(n-1, k) = T(n, k)
%F A102426 T(n, k)=binomial(floor(n/2)+k, floor((n-1)/2-k) - Paul Barry (pbarry(AT)wit.ie), 
               Jun 22 2005
%e A102426 The first few polynomials are:
%e A102426 0
%e A102426 1
%e A102426 1
%e A102426 x + 1
%e A102426 2x + 1
%e A102426 x^2 + 3x + 1
%e A102426 3x^2 + 4x + 1
%Y A102426 Upward diagonals sums are A062200. Downward rows are A102427. Row sums 
               are A000045. Row terms reversed = A011973. Also A102427, A102428, 
               A102429.
%Y A102426 Sequence in context: A121560 A136405 A035667 this_sequence A092865 A098925 
               A052920
%Y A102426 Adjacent sequences: A102423 A102424 A102425 this_sequence A102427 A102428 
               A102429
%K A102426 easy,nonn,tabf
%O A102426 0,6
%A A102426 Russell Walsmith (russw(AT)lycos.com), Jan 08 2005