%I A089177
%S A089177 1,1,1,1,2,1,1,3,2,1,4,4,1,1,5,6,2,1,6,9,4,1,7,12,6,1,8,16,10,1,1,9,20,
%T A089177 14,2,1,10,25,20,4,1,11,30,26,6,1,12,36,35,10,1,13,42,44,14,1,14,49,56,
%U A089177 20,1,15,56,68,26,1,16,64,84,36,1,1,17,72,100,46,2,1,18,81,120,60,4,1
%N A089177 Triangle read by rows: T(n,k) (n >= 0, 0 <= k <= 1+log_2(floor(n)) giving 
               number of non-squashing partitions of n into k parts.
%H A089177 N. J. A. Sloane and J. A. Sellers, <a href="http://arXiv.org/abs/math.CO/
               0312418">On non-squashing partitions</a>, Discrete Math., 294 (2005), 
               259-274.
%F A089177 Row 0 = {1}, row 1 = {1 1}; for n >=2, row n = row n-1 + (row floor(n/
               2) shifted one place right).
%F A089177 G.f. for column k (k >= 2): x^(2^(k-2))/((1-x)*Product_j=1..k-2} (1-x^(2^j))).
%e A089177 Triangle begins:
%e A089177 1
%e A089177 1 1
%e A089177 1 2 1
%e A089177 1 3 2
%e A089177 1 4 4 1
%e A089177 1 5 6 2
%e A089177 1 6 9 4
%e A089177 1 7 12 6
%e A089177 1 8 16 10 1
%Y A089177 Cf. A089178. Columns give A002620, A008804, A088932, A088954. Row sums 
               give A000123.
%Y A089177 Sequence in context: A094363 A124832 A137569 this_sequence A023996 A049998 
               A029253
%Y A089177 Adjacent sequences: A089174 A089175 A089176 this_sequence A089178 A089179 
               A089180
%K A089177 nonn,tabf,easy
%O A089177 0,5
%A A089177 N. J. A. Sloane (njas(AT)research.att.com), Dec 08 2003
%E A089177 More terms from Alford Arnold (Alford1940(AT)aol.com), May 22 2004