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A066448
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Triangle T(n,k) giving number of basis partitions of n with a Durfee square of order k (n >= 0, 0 <= k <= n).
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3
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1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 2, 10, 1, 0, 0, 0, 0, 0, 0, 0, 2, 12, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 14, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,5
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LINKS
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J. M. Nolan, C. D. Savage and H. S. Wilf, Basis partitions, Discrete Math. 179 (1998), 277-283.
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 2, 0;
0, 2, 0, 0;
0, 2, 1, 0, 0;
0, 2, 2, 0, 0, 0;
0, 2, 4, 0, 0, 0, 0;
0, 2, 6, 0, 0, 0, 0, 0;
0, 2, 8, 0, 0, 0, 0, 0, 0;
...
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MAPLE
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T := proc(n, d); option remember; if n=0 and d=0 then RETURN(1) elif n<=0 or d<=0 then RETURN(0) else RETURN(T(n-d, d)+T(n-2*d+1, d-1)+T(n-3*d+1, d-1)) fi:
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PROG
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(PARI) T(n, k)=if(k<0||k>n, 0, if(k==0, n==0, T(n-k, k)+T(n-2*k+1, k-1)+T(n-3*k+1, k-1))) /* Michael Somos, Mar 10 2004 */
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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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