A059883 - OEIS

A059883

As upper right triangle: descending wiggly sums to n where first term is k (sums in which terms alternately decrease and increase; zagzig partitions).

%I #8 Jan 20 2022 18:02:35

%S 1,0,1,0,1,1,0,0,1,1,0,1,1,1,1,0,2,1,1,1,1,0,2,2,2,1,1,1,0,4,3,2,2,1,

%T 1,1,0,6,6,3,3,2,1,1,1,0,9,9,6,3,3,2,1,1,1,0,14,13,10,6,4,3,2,1,1,1,0,

%U 23,21,15,10,6,4,3,2,1,1,1,0,35,33,24,15,10,7,4,3,2,1,1,1,0,55,52,38,25,15,10,7,4,3,2,1,1,1

%N As upper right triangle: descending wiggly sums to n where first term is k (sums in which terms alternately decrease and increase; zagzig partitions).

%H Alois P. Heinz, <a href="/A059883/b059883.txt">Rows n = 1..200, flattened</a>

%F If n>k>0 T(n, k)=sum_j[S(n-k, j)] over k>j and if n>0 T(n, n)=1; where S(n, k)=A059882(n, k) and if n>k>0, S(n, k)=sum_j[T(n-k, j)] over j>k (note reversal) and if n>0 S(n, n)=1.

%e Rows start (1,0,0,0,0,...), (1,1,0,1,...), (1,1,1,...) etc. T(10,4)=6 since 10 can be written as 4+2+4, 4+2+3+1, 4+1+5, 4+1+4+1, 4+1+3+2, or 4+1+2+1+2.

%Y Column sums are A025049. Cf. A025047, A025048, A059881, A059882.

%K nonn,tabl

%O 1,17

%A _Henry Bottomley_, Feb 05 2001