Search: id:A117195
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%I A117195
%S A117195 1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,1,1,0,1,0,1,1,1,1,1,0,
%T A117195 1,0,1,1,2,1,1,1,0,1,1,0,2,1,2,1,1,1,0,1,0,1,1,2,2,2,1,1,1,0,1,0,1,2,2,
%U A117195 2,2,2,1,1,1,0,1,0,1,1,3,2,3,2,2,1,1,1,0,1,0,1,2,2,4,2,3,2,2,1,1,1,0,1
%N A117195 Triangle read by rows: T(n,k) = number of partitions into distinct parts 
               having rank k, 0<=k<n.
%C A117195 T(n,0) = A010054(n), T(n,1) = 1-A010054(n) for n>1;
%C A117195 A000009(n) = Sum(T(n,k): 0<=k<n);
%C A117195 A117192(n) = Sum(T(n,k)*(1 - k mod 2): 0<=k<n);
%C A117195 A117193(n) = Sum(T(n,k)*(k mod 2): 0<=k<n);
%C A117195 A117194(n) = Sum(T(n,k)*(1 - k mod 2): 0<k<n);
%e A117195 T(12,0) = #{} = 0,
%e A117195 T(12,1) = #{5+4+2+1} = 1,
%e A117195 T(12,2) = #{6+3+2+1, 5+4+3} = 2,
%e A117195 T(12,3) = #{6+5+1, 6+4+2} = 2,
%e A117195 T(12,4) = #{7+4+1, 7+3+2} = 2,
%e A117195 T(12,5) = #{8+3+1, 7+5} = 2,
%e A117195 T(12,6) = #{9+2+1, 8+4} = 2,
%e A117195 T(12,7) = #{9+3} = 1,
%e A117195 T(12,8) = #{10+2} = 1,
%e A117195 T(12,9) = #{11+1} = 1,
%e A117195 T(12,10) = #{} = 0,
%e A117195 T(12,11) = #{12} = 1.
%Y A117195 Cf. A063995, A105806.
%Y A117195 Sequence in context: A037907 A037801 A053252 this_sequence A156606 A107034 
               A117410
%Y A117195 Adjacent sequences: A117192 A117193 A117194 this_sequence A117196 A117197 
               A117198
%K A117195 nonn,tabl
%O A117195 1,40
%A A117195 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 03 2006

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