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A371300 Triangle read by rows: Riordan array (1/(1 - x), (1 + x)/(1 - x - x^2)).

%I A371300 #16 Apr 22 2024 13:42:32
%S A371300 1,1,2,1,5,4,1,10,16,8,1,18,45,44,16,1,31,107,158,112,32,1,52,232,461,
%T A371300 488,272,64,1,86,474,1190,1680,1392,640,128,1,141,930,2831,5009,5512,
%U A371300 3760,1472,256,1,230,1772,6355,13541,18602,16816,9760,3328,512
%N A371300 Triangle read by rows: Riordan array (1/(1 - x), (1 + x)/(1 - x - x^2)).
%F A371300 T(n, k) = 2*T(n-1, k-1) + T(n-1, k) + T(n-2, k-1) + T(n-2, k), T(n, k) = 0 if k > n or if k < 0, T(n, 0) = 1. - _Philippe Deléham_ , Apr 22 2024
%e A371300 Triangle begins:
%e A371300   [0] 1;
%e A371300   [1] 1,  2;
%e A371300   [2] 1,  5,   4;
%e A371300   [3] 1, 10,  16,    8;
%e A371300   [4] 1, 18,  45,   44,   16;
%e A371300   [5] 1, 31, 107,  158,  112,   32;
%e A371300   [6] 1, 52, 232,  461,  488,  272,   64;
%e A371300   [7] 1, 86, 474, 1190, 1680, 1392,  640,  128;
%p A371300 T := proc(n, k) option remember; if k > n or k < 0 then 0 elif k = 0 then 1 else
%p A371300 2*T(n-1, k-1) + T(n-1, k) + T(n-2, k-1) + T(n-2, k) fi end:
%p A371300 for n from 0 to 9 do seq(T(n, k), k = 0..n) od;  # _Peter Luschny_, Apr 22 2024
%o A371300 (SageMath)  # using function riordan_array from A256893
%o A371300 riordan_array(1/(1 - x), (1 + x)/(1 - x - x^2), 8)
%Y A371300 Cf. A371301 (row sums), A370174, A256893.
%K A371300 nonn,tabl,easy
%O A371300 0,3
%A A371300 _Peter Luschny_, Mar 18 2024