|
Search: id:A062110
|
|
|
| A062110 |
|
Table read by antidiagonals where T(n,k) is coefficient of x^k in (1-x)^n/(1-2x)^n. |
|
+0
4
|
|
| 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 5, 3, 1, 0, 8, 12, 9, 4, 1, 0, 16, 28, 25, 14, 5, 1, 0, 32, 64, 66, 44, 20, 6, 1, 0, 64, 144, 168, 129, 70, 27, 7, 1, 0, 128, 320, 416, 360, 225, 104, 35, 8, 1, 0, 256, 704, 1008, 968, 681, 363, 147, 44, 9, 1, 0, 512, 1536, 2400, 2528, 1970
(list; table; graph; listen)
|
|
|
OFFSET
|
0,8
|
|
|
FORMULA
|
T(n, k)=T(n-1, k)+sum{j<k}[T(n, j)] with T(0, k)=0^k.
G.f.: 1/(1-x(1-y)/(1-2y)) = Sum_{i, j} a(i, j)x^i*y^j.
T(n,k)=A121462(n+1,k+1)*2^(n-2*k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 01 2006
|
|
EXAMPLE
|
Rows start (1,0,0,0,0,...), (1,1,2,4,8,...), (1,2,5,12,28,...), etc.
|
|
PROGRAM
|
(PARI) a(i, j)=if(i<0|j<0, 0, polcoeff(((1-x)/(1-2*x)+x*O(x^j))^i, j))
|
|
CROSSREFS
|
Rows include A000007, A011782, A045623, A058396, A062109. Columns include A000012, A001477, A000096, A000297. Main diagonal is A002002. T(n, k) is a multiple of 2^(k-n), dividing by this gives a table similar to A050143 except at the edges.
Essentially the same array as A105306.
Sequence in context: A071510 A110124 A116389 this_sequence A122896 A107267 A112161
Adjacent sequences: A062107 A062108 A062109 this_sequence A062111 A062112 A062113
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Henry Bottomley (se16(AT)btinternet.com), May 30 2001
|
|
|
Search completed in 0.002 seconds
|
