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A091562 Triangle read by rows, related to Pascal's triangle, starting with 1, 0, 0.

%I A091562 #10 Oct 27 2021 15:03:02
%S A091562 1,0,0,1,1,1,1,2,2,1,2,5,7,5,2,3,10,17,17,10,3,5,20,41,51,41,20,5,8,
%T A091562 38,91,136,136,91,38,8,13,71,195,339,405,339,195,71,13,21,130,403,799,
%U A091562 1107,1107,799,403,130,21,34,235,812,1807,2845,3297,2845,1807,812,235,34
%N A091562 Triangle read by rows, related to Pascal's triangle, starting with 1, 0, 0.
%F A091562 T(n, k) = T(n-1, k) + T(n-1, k-1) + T(n-2, k) + T(n-2, k-1) + T(n-2, k-2) for n >= 2, k >= 0, with initial conditions specified by first two rows.
%F A091562 G.f.: A(x, y) = (1-x-x*y)/(1-x-x*y-x^2-x^2*y-x^2*y^2).
%e A091562 Triangle begins:
%e A091562   1;
%e A091562   0,0;
%e A091562   1,1,1;
%e A091562   1,2,2,1;
%e A091562   2,5,7,5,2;
%e A091562   ...
%Y A091562 Row sums: A054878, column 0: A000045(n-1), column 1: A001629.
%Y A091562 Cf. A090171, A090172, A090173, A090174, A091533, A205575 (same recurrence).
%Y A091562 Cf. A090172.
%K A091562 nonn,easy,tabl
%O A091562 0,8
%A A091562 _Christian G. Bower_, Jan 20 2004