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A066448
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Triangle T(n,k) giving number of basic partitions of n with a Durfee square of order k (n >= 0, 0 <= k <= n).
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1
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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, 0, 2, 18, 12, 0, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| J. M. Nolan, C. D. Savage and H. S. Wilf, Basis partitions, Discrete Math. 179 (1998), 277-283.
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EXAMPLE
| 1; 0,1; 0,2,0; 0,2,0,0; 0,2,1,0,0; ...
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MAPLE
| 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
| (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
| Sequence in context: A112301 A134013 A136521 * A108497 A108498 A178923
Adjacent sequences: A066445 A066446 A066447 * A066449 A066450 A066451
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 29 2001
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