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A289971 Number of permutations of [n] determined by their antidiagonal sums. 3
1, 1, 2, 4, 9, 20, 49, 114, 277, 665, 1608, 3875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..11.

C. Bebeacua, T. Mansour, A. Postnikov, S. Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.

FindStat - Combinatorial Statistic Finder, The number of permutations with the same antidiagonal sums.

PROG

(Sage)

def X_ray(pi):

    P = Permutation(pi).to_matrix()

    n = P.nrows()

    return tuple(sum(P[k-1-j][j] for j in range(max(0, k-n), min(k, n)))

                 for k in range(1, 2*n))

@cached_function

def X_rays(n):

    return sorted(X_ray(pi) for pi in Permutations(n))

def statistic(pi): return X_rays(pi.size()).count(X_ray(pi))

[[statistic(pi) for pi in Permutations(n)].count(1) for n in range(7)]

CROSSREFS

Cf. A019589, A002047, A290279, A290280.

Sequence in context: A123467 A124497 A286983 * A093637 A068051 A032289

Adjacent sequences:  A289968 A289969 A289970 * A289972 A289973 A289974

KEYWORD

nonn,more

AUTHOR

Martin Rubey, Jul 16 2017

EXTENSIONS

a(8)-a(11) from Alois P. Heinz, Jul 24 2017

STATUS

approved

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Last modified October 17 01:30 EDT 2018. Contains 316275 sequences. (Running on oeis4.)