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A105474 Triangle read by rows: T(n,k) is number of compositions of n into k parts when each odd part can be of two kinds.

%I A105474 #3 Mar 30 2012 17:36:01
%S A105474 2,1,4,2,4,8,1,9,12,16,2,8,30,32,32,1,14,37,88,80,64,2,12,66,136,240,
%T A105474 192,128,1,19,75,257,440,624,448,256,2,16,116,352,890,1312,1568,1024,
%U A105474 512,1,24,126,564,1401,2844,3696,3840,2304,1024,2,20,180,720,2370,5004
%N A105474 Triangle read by rows: T(n,k) is number of compositions of n into k parts when each odd part can be of two kinds.
%F A105474 G.f.=tz(2+z)/(1-2tz-z^2-tz^2).
%e A105474 T(4,2)=9 because we have (1,3),(1',3),(1,3'),(1',3'),(3,1),(3',1),(3,1'),(3',1') and (2,2).
%e A105474 Triangle begins:
%e A105474 2;
%e A105474 1,4;
%e A105474 2,4,8;
%e A105474 1,9,12,16;
%e A105474 2,8,30,32,32;
%p A105474 G:=t*z*(2+z)/(1-2*t*z-z^2-t*z^2): Gser:=simplify(series(G,z=0,14)): for n from 1 to 12 do P[n]:=sort(coeff(Gser,z^n)) od: for n from 1 to 12 do seq(coeff(P[n],t^k),k=1..n) od; # yields sequence in triangular form
%Y A105474 Row sums yield A052945.
%K A105474 nonn,tabl
%O A105474 1,1
%A A105474 _Emeric Deutsch_, Apr 09 2005