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.

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, 192, 128, 1, 19, 75, 257, 440, 624, 448, 256, 2, 16, 116, 352, 890, 1312, 1568, 1024, 512, 1, 24, 126, 564, 1401, 2844, 3696, 3840, 2304, 1024, 2, 20, 180, 720, 2370, 5004

Offset: 1

Author

Emeric Deutsch, Apr 09 2005

Keywords

• nonn
• tabl

Examples

			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).
Triangle begins:
2;
1,4;
2,4,8;
1,9,12,16;
2,8,30,32,32;
		

Crossrefs

Row sums yield A052945.

Programs

Maple

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

Formula

G.f.=tz(2+z)/(1-2tz-z^2-tz^2).