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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 12:33 EST 2019. Contains 329916 sequences. (Running on oeis4.)