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A371300
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Triangle read by rows: Riordan array (1/(1 - x), (1 + x)/(1 - x - x^2)).
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1
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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EXAMPLE
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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;
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MAPLE
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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
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PROG
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(SageMath) # using function riordan_array from A256893
riordan_array(1/(1 - x), (1 + x)/(1 - x - x^2), 8)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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