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A276696
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Triangle read by rows, T(n,k) = T(n-1, k-1) + T(n-2, k) if k is odd, T(n-1, k-1) + T(n-1, k) if k is even, for k<=0<=n and n>=2 with T(0,0)=T(1,0)=T(1,1)=0 and T(n,k)=0 when k>n, k<0, or n<0.
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0
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1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 6, 5, 3, 1, 1, 3, 9, 8, 8, 3, 1, 1, 4, 12, 14, 16, 9, 4, 1, 1, 4, 16, 20, 30, 19, 13, 4, 1, 1, 5, 20, 30, 50, 39, 32, 14, 5, 1, 1, 5, 25, 40, 80, 69, 71, 36, 19, 5, 1, 1, 6, 30, 55, 120, 119, 140, 85, 55, 20, 6, 1
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OFFSET
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0,8
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COMMENTS
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This is the triangle frst(n,k) in the Ehrenborg and Readdy link. See Definition 3.1 and Table 1.
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LINKS
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EXAMPLE
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Triangle starts:
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 2, 4, 2, 1;
1, 3, 6, 5, 3, 1;
1, 3, 9, 8, 8, 3, 1;
...
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MATHEMATICA
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T[n_, n_] = T[_, 0] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = If[OddQ[k], T[n-1, k-1] + T[n-2, k], T[n-1, k-1] + T[n-1, k]]; T[_, _] = 0;
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PROG
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(PARI) frst(n, k) = if ((k>n) || (n<0) || (k<0), 0, if (n<=2, 1, if (k==0, 1, if (k%2, frst(n-1, k-1) + frst(n-2, k), frst(n-1, k-1) + frst(n-1, k)))));
tf(nn) = for (n=0, nn, for (k=0, n, print1(frst(n, k), ", "); ); print(); );
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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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