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A205575
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Triangle read by rows, related to Pascal's triangle.
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4
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1, 1, 0, 2, 2, 1, 3, 5, 4, 1, 5, 12, 14, 8, 2, 8, 25, 38, 32, 15, 3, 13, 50, 94, 104, 71, 28, 5, 21, 96, 215, 293, 260, 149, 51, 8, 34, 180, 468, 756, 822, 612, 304, 92, 13, 55, 331, 980, 1828, 2346, 2136, 1376, 604, 164, 21
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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Similar to A091533 and to A091562. Triangle satisfying the same recurrence as A091533 and A091562, but with the initial values T(0,0) = 1, T(0,1) = 1, T(1,1) = 0.
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LINKS
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FORMULA
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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. T(0,0) = 1, T(1,0) = 1, T(1,1) = 0.
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EXAMPLE
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Triangle begins :
1
1, 0
2, 2, 1
3, 5, 4, 1
5, 12, 14, 8, 2
8, 25, 38, 32, 15, 3
13, 50, 94, 104, 71, 28, 5
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PROG
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(PARI) T(n, k) = {if(n<0, return(0)); if (n==0, if (k<0, return(0)); if (k==0, return(1))); if (n==1, if (k<0, return(0)); if (k==0, return(1)); if (k==1, return(0))); T(n-1, k)+T(n-1, k-1)+T(n-2, k)+T(n-2, k-1)+T(n-2, k-2); } \\ Michel Marcus, Oct 27 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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