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

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, 488, 272, 64, 1, 86, 474, 1190, 1680, 1392, 640, 128, 1, 141, 930, 2831, 5009, 5512, 3760, 1472, 256, 1, 230, 1772, 6355, 13541, 18602, 16816, 9760, 3328, 512

Offset: 0

Author

Peter Luschny, Mar 18 2024

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
  [0] 1;
  [1] 1,  2;
  [2] 1,  5,   4;
  [3] 1, 10,  16,    8;
  [4] 1, 18,  45,   44,   16;
  [5] 1, 31, 107,  158,  112,   32;
  [6] 1, 52, 232,  461,  488,  272,   64;
  [7] 1, 86, 474, 1190, 1680, 1392,  640,  128;
		

Crossrefs

Cf. A371301 (row sums), A370174, A256893.

Programs

Maple

T := proc(n, k) option remember; if k > n or k < 0 then 0 elif k = 0 then 1 else
2*T(n-1, k-1) + T(n-1, k) + T(n-2, k-1) + T(n-2, k) fi end:
for n from 0 to 9 do seq(T(n, k), k = 0..n) od;  # Peter Luschny, Apr 22 2024

SageMath

# using function riordan_array from A256893
riordan_array(1/(1 - x), (1 + x)/(1 - x - x^2), 8)

Formula

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