%I A072170
%S A072170 1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,3,2,2,1,1,1,2,3,2,2,1,1,1,3,3,4,2,
%T A072170 2,1,1,1,1,4,3,4,2,2,1,1,1,4,4,5,4,4,2,2,1,1,1,3,5,4,5,4,4,2,2,1,1,
%U A072170 1,5,6,8,5,6,4,4,2,2,1,1,1,2,6,6,8,5,6,4,4,2,2,1,1,1,5,6,9,8,9,6,6
%N A072170 Square array T(n,k) (n >= 0, k >= 2) read by antidiagonals, where T(n,
               k) is the number of ways of writing n as Sum_{i=0..inf} c_i 2^i, 
               c_i in {0,1,...,k-1}.
%C A072170 k-th column is k-th binary partition function.
%D A072170 B. Reznick, Some binary partition functions, in "Analytic number theory" 
               (Conf. in honor P. T. Bateman, Allerton Park, IL, 1989), 451-477, 
               Progr. Math., 85, Birkhaeuser Boston, Boston, MA, 1990.
%e A072170 Array begins:
%e A072170 1 1 1 1 1 1 1 1 ...
%e A072170 1 1 1 1 1 1 1 1 ...
%e A072170 1 2 2 2 2 2 2 2 ...
%e A072170 1 1 2 2 2 2 2 2 ...
%e A072170 1 2 3 3 4 4 4 4 ...
%e A072170 1 3 4 5 5 6 6 6 ...
%Y A072170 k=3 column is A002487, k=4 is integers doubled up, k=5, 6, 7 are A007728, 
               A007729, A007730, limiting (infinity) column is A000123 doubled up.
%Y A072170 Sequence in context: A151683 A133912 A122934 this_sequence A056624 A093997 
               A157196
%Y A072170 Adjacent sequences: A072167 A072168 A072169 this_sequence A072171 A072172 
               A072173
%K A072170 nonn,tabl
%O A072170 0,8
%A A072170 N. J. A. Sloane (njas(AT)research.att.com), Jun 29 2002