|
Search: id:A105478
|
|
|
| A105478 |
|
Triangle read by rows: T(n,k) is the number of compositions of n into k parts when parts 1 and 2 are of two kinds. |
|
+0
2
|
|
| 2, 2, 4, 1, 8, 8, 1, 8, 24, 16, 1, 8, 36, 64, 32, 1, 9, 44, 128, 160, 64, 1, 10, 54, 192, 400, 384, 128, 1, 11, 66, 264, 720, 1152, 896, 256, 1, 12, 79, 352, 1120, 2432, 3136, 2048, 512, 1, 13, 93, 456, 1632, 4272, 7616, 8192, 4608, 1024, 1, 14, 108, 576, 2280, 6816
(list; table; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
FORMULA
|
G.f.=tz(2-z^2)/(1-z-2tz+tz^3). T(n, k)=T(n-1, k)+2T(n-1, k-1)-T(n-3, k-1).
|
|
EXAMPLE
|
T(4,2)=8 because we have (1,3),(1',3),(3,1),(3,1'),(2,2),(2,2'),(2',2) and (2',2').
Triangle begins:
2;
2,4;
1,8,8;
1,8,24,16;
1,8,36,64,32;
|
|
MAPLE
|
G:=t*z*(2-z^2)/(1-z-2*t*z+t*z^3): Gser:=simplify(series(G, z=0, 14)): for n from 1 to 12 do P[n]:=expand(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 A052536.
Sequence in context: A070306 A014665 A055035 this_sequence A114427 A129355 A080963
Adjacent sequences: A105475 A105476 A105477 this_sequence A105479 A105480 A105481
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 10 2005
|
|
|
Search completed in 0.002 seconds
|
