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A099793 Table read by rows where row n consists of 2n terms representing k-matches 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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified August 2 01:19 EDT 2021. Contains 346408 sequences. (Running on oeis4.)