|
Search: id:A059283
|
|
|
| A059283 |
|
Triangle T(n,k) (0<= k <=n) read by rows. Left edge is 1, 0, 0, ... Otherwise each entry is sum of entry to left, entries immediately above it to left and right and entry directly above it 2 rows back. |
|
+0
3
|
|
| 1, 0, 1, 0, 2, 3, 0, 2, 8, 11, 0, 2, 14, 36, 47, 0, 2, 20, 78, 172, 219, 0, 2, 26, 138, 424, 862, 1081, 0, 2, 32, 216, 856, 2314, 4476, 5557, 0, 2, 38, 312, 1522, 5116, 12768, 23882, 29439, 0, 2, 44, 426, 2476, 9970, 30168, 71294, 130172, 159611, 0, 2, 50, 558
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
FORMULA
|
T(0, 0)=1; T(n, 0)=0, n>0; T(n, k)=T(n, k-1)+T(n-1, k-1)+T(n-1, k)+T(n-2, k-1), n, k>0
G.f. for T(n, k): ((1+2*w+w^2)*z^2+(-1-2*w-w^2)*z-w*(-3*w^2-6*w+1)^(1/2)+2*w)/(1+w)^2/((1+w)*z^2+(w-1)*z+w) (expand first as series in z, then in w).
|
|
EXAMPLE
|
1; 0,1; 0,2,3; 0,2,8,11; 0,2,14,36,47; ... [36 = 14 + 8 + 11 + 3 for example].
|
|
CROSSREFS
|
Right edge is A059284. Cf. A059226.
Sequence in context: A024307 A002392 A002708 this_sequence A128621 A132385 A089235
Adjacent sequences: A059280 A059281 A059282 this_sequence A059284 A059285 A059286
|
|
KEYWORD
|
nonn,tabl,easy,nice
|
|
AUTHOR
|
njas, Jan 24 2001
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), Jan 25 2001
|
|
|
Search completed in 0.002 seconds
|
