

A099793


Table read by rows where row n consists of 2n terms representing kmatches described in A098813.


0



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
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OFFSET

1,3


COMMENTS

For a string of letters of length k, say abc...def, let f(k) be the string of length k1 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<=2n1.


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: A073027 A278986 A292159 * A273895 A086329 A294118
Adjacent sequences: A099790 A099791 A099792 * A099794 A099795 A099796


KEYWORD

nonn,tabf


AUTHOR

Zerinvary Lajos and Ray Chandler, Oct 26 2004


STATUS

approved



