|
Search: id:A049600
|
|
|
| A049600 |
|
Array T read by diagonals; T(i,j)=number of paths from (0,0) to (i,j) consisting of nonvertical segments (x(k),y(k))-to-(x(k+1),y(k+1)) such that 0=x(1)<x(2)<...<x(n-1)<x(n)=i, 0=y(1)<=y(2)<=...y(n-1)<=y(n)=j, for i >= 0, j >= 0. |
|
+0
22
|
|
| 0, 0, 1, 0, 1, 2, 0, 1, 3, 4, 0, 1, 4, 8, 8, 0, 1, 5, 13, 20, 16, 0, 1, 6, 19, 38, 48, 32, 0, 1, 7, 26, 63, 104, 112, 64, 0, 1, 8, 34, 96, 192, 272, 256, 128, 0, 1, 9, 43, 138, 321, 552, 688, 576, 256, 0, 1, 10, 53, 190, 501, 1002, 1520, 1696, 1280, 512, 0, 1, 11, 64, 253, 743
(list; table; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
Essentially array A059576 divided by sequence A011782
|
|
FORMULA
|
T(n,k) = Sum_{j=0..n-1} C(k+j,j)*C(n-1,j). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 06 2006
|
|
EXAMPLE
|
Diagonals (each starting on row 1): {0}; {0,1}; {0,1,2}; ...
|
|
PROGRAM
|
(PARI) A(i, j)=polcoeff(x/(1-2*x)*((1-x)/(1-2*x))^j+x*O(x^i), i) (from Michael Somos)
(PARI) T(n, k)=sum(j=0, n-1, binomial(k+j, j)*binomial(n-1, j)) - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 06 2006
|
|
CROSSREFS
|
Diagonal sums are even-indexed Fibonacci numbers. Alternating (+-) diagonal sums are signed Fibonacci numbers.
T(n, n-1) = A001850(n) (Delannoy numbers). T(n, n)=A047781. Cf. A035028, A055587.
Sequence in context: A068920 A099390 A124031 this_sequence A004542 A134405 A091612
Adjacent sequences: A049597 A049598 A049599 this_sequence A049601 A049602 A049603
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
Search completed in 0.003 seconds
|
