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

Author

Zerinvary Lajos and Ray Chandler, Oct 26 2004

Keywords

• nonn
• tabf

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.

Examples

			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.