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A371300
Triangle read by rows: Riordan array (1/(1 - x), (1 + x)/(1 - x - x^2)).
1
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
0,3
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
EXAMPLE
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;
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
PROG
(SageMath) # using function riordan_array from A256893
riordan_array(1/(1 - x), (1 + x)/(1 - x - x^2), 8)
CROSSREFS
Cf. A371301 (row sums), A370174, A256893.
Sequence in context: A092821 A238241 A299444 * A110552 A129161 A103415
KEYWORD
nonn,tabl,easy
AUTHOR
Peter Luschny, Mar 18 2024
STATUS
approved