|
Search: id:A123519
|
|
|
| A123519 |
|
Triangle read by rows: T(n,k) number of tilings of a 2n X 3 grid by dominoes, 2k of which are in a vertical position (0<=k<=n). |
|
+0
2
|
|
| 1, 1, 2, 1, 6, 4, 1, 12, 20, 8, 1, 20, 60, 56, 16, 1, 30, 140, 224, 144, 32, 1, 42, 280, 672, 720, 352, 64, 1, 56, 504, 1680, 2640, 2112, 832, 128, 1, 72, 840, 3696, 7920, 9152, 5824, 1920, 256, 1, 90, 1320, 7392, 20592, 32032, 29120, 15360, 4352, 512, 1, 110
(list; table; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Sum of terms in row n = A001835(n+1). Sum(k*T(n,k), k=0..n)=A123520(n) (n>=1).
|
|
FORMULA
|
T(n,k)=2^k*binom(n+k,2k). G.f.=(1-z)/(1-2z+z^2-2tz).
|
|
EXAMPLE
|
T(1,1)=2 because a 2 X 3 grid can be tiled in 2 ways with dominoes so that exactly 2 dominoes are in vertical position: place a horizontal domino above or below two adjacent vertical dominoes.
|
|
MAPLE
|
T:=(n, k)->2^k*binomial(n+k, 2*k): for n from 0 to 10 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
|
|
CROSSREFS
|
Cf. A001835, A123520.
Sequence in context: A135994 A133166 A051482 this_sequence A114687 A137594 A112360
Adjacent sequences: A123516 A123517 A123518 this_sequence A123520 A123521 A123522
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 16 2006
|
|
|
Search completed in 0.002 seconds
|
