cp's OEIS Frontend

A066448 Triangle T(n,k) giving number of basis partitions of n with a Durfee square of order k (n >= 0, 0 <= k <= n).

%I A066448 #28 Jan 13 2022 09:54:16
%S A066448 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,
%T A066448 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,
%U A066448 2,14,4,0,0,0,0,0,0,0,0,0,2,16,8,0,0,0,0,0,0,0,0,0
%N A066448 Triangle T(n,k) giving number of basis partitions of n with a Durfee square of order k (n >= 0, 0 <= k <= n).
%H A066448 Seiichi Manyama, <a href="/A066448/b066448.txt">Rows n = 0..139, flattened</a>
%H A066448 J. M. Nolan, C. D. Savage and H. S. Wilf, <a href="https://doi.org/10.1016/s0012-365x(97)00101-5">Basis partitions</a>, Discrete Math. 179 (1998), 277-283.
%e A066448 Triangle begins:
%e A066448   1;
%e A066448   0, 1;
%e A066448   0, 2, 0;
%e A066448   0, 2, 0, 0;
%e A066448   0, 2, 1, 0, 0;
%e A066448   0, 2, 2, 0, 0, 0;
%e A066448   0, 2, 4, 0, 0, 0, 0;
%e A066448   0, 2, 6, 0, 0, 0, 0, 0;
%e A066448   0, 2, 8, 0, 0, 0, 0, 0, 0;
%e A066448   ...
%p A066448 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:
%o A066448 (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 */
%Y A066448 Row sums give A066447.
%K A066448 nonn,tabl
%O A066448 0,5
%A A066448 _N. J. A. Sloane_, Dec 29 2001