A099793 Table read by rows where row n consists of 2n terms representing k-matches described in A098813.

1, 1, 4, 1, 0, 1, 9, 4, 5, 1, 0, 1, 21, 19, 12, 9, 7, 1, 0, 1, 52, 57, 53, 47, 16, 16, 9, 1, 0, 1, 127, 178, 202, 154, 120, 85, 20, 25, 11, 1, 0, 1, 313, 543, 664, 636, 525, 310, 233, 133, 24, 36, 13, 1, 0, 1, 778, 1591, 2204, 2355, 2007, 1621, 1076, 549, 404, 191, 28, 49, 15

Offset

1,3

Comments

For a string of letters of length k, say abc...def, let f(k) be the string of length k-1 consisting of the adjacent pairs ab, bc, cd, ..., de, ef. Given n, let U be the string of length 2n consisting of n 1's followed by n 2's: 11...122...2. Then T(n,k) = number of the C(2n,n) permutations V of U such that f(U) and f(V) agree in exactly k places, 0<=k<=2n-1.

Links

Table of n, a(n) for n=1..69.

Example

Table begins:
1: 1,1,
2: 4,1,0,1,
3: 9,4,5,1,0,1,
4: 21,19,12,9,7,1,0,1,
5: 52,57,53,47,16,16,9,1,0,1,
6: 127,178,202,154,120,85,20,25,11,1,0,1,
7: 313,543,664,636,525,310,233,133,24,36,13,1,0,1,
8: 778,1591,2204,2355,2007,1621,1076,549,404,191,28,49,15,1,0,1,
9: 1941,4598,7091,8223,8036,6722,4721,3457,1911,901,645,259,32,64,17,1,0,1

Crossrefs

First column is A051292(n+1); second column is A098813; row sums = A000984.

Sequence in context: A370073 A278986 A292159 * A273895 A363044 A086329

Adjacent sequences: A099790 A099791 A099792 * A099794 A099795 A099796

Keyword

nonn,tabf

Author

Zerinvary Lajos and Ray Chandler, Oct 26 2004

Status

approved