|
Search: id:A059474
|
|
|
| A059474 |
|
Triangle read by rwos: T(n,k) = coefficient of x^n*y^k in 1/(1-2*z-2*w+2*z*w) read by rows in order 00, 10, 01, 20, 11, 02, ... |
|
+0
2
|
|
| 1, 2, 2, 4, 6, 4, 8, 16, 16, 8, 16, 40, 52, 40, 16, 32, 96, 152, 152, 96, 32, 64, 224, 416, 504, 416, 224, 64, 128, 512, 1088, 1536, 1536, 1088, 512, 128, 256, 1152, 2752, 4416, 5136, 4416, 2752, 1152, 256, 512, 2560, 6784, 12160, 16032, 16032
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Pascal-like triangle: start with 1 at top; every subsequent entry is the sum of everything above you, plus 1.
|
|
FORMULA
|
G.f.: 1/(1-2*z-2*w+2*z*w).
T(n, k) = Sum_{b=0..n} (-1)^b*2^(n+k-b)*C(n, b)*C(n+k-b, n).
|
|
EXAMPLE
|
1; 2,2; 4,6,4; 8,16,16,8; ...
|
|
MAPLE
|
read transforms; SERIES2(1/(1-2*z-2*w+2*z*w), x, y, 12): SERIES2TOLIST(%, x, y, 12);
|
|
CROSSREFS
|
See A059576 for a similar triangle.
Sequence in context: A097089 A096466 A088965 this_sequence A078099 A118960 A107797
Adjacent sequences: A059471 A059472 A059473 this_sequence A059475 A059476 A059477
|
|
KEYWORD
|
nonn,tabl,easy
|
|
AUTHOR
|
njas, Feb 03, 2001; revised Jun 12 2005
|
|
|
Search completed in 0.002 seconds
|
