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

1,1

Links

Table of n, a(n) for n=1..61.

Formula

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

Example

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;

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

Crossrefs

Row sums yield A052945.

Sequence in context: A205509 A118736 A201161 * A216568 A219432 A120988

Adjacent sequences: A105471 A105472 A105473 * A105475 A105476 A105477

Keyword

nonn,tabl

Author

Emeric Deutsch, Apr 09 2005

Status

approved