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A181194 Number of n X 7 matrices containing a permutation of 1..n*7 in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally. 2
1, 132, 49100, 25097600, 14083834704, 8092149471168, 4673805856338368, 2702482348019033600, 1562998915785444034816, 904016986809953084011520, 522876616523380188491377664, 302428597238403007787949047808 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 7 of A181196.

LINKS

R. H. Hardin, Table of n, a(n) for n=1..100

FORMULA

Empirical: a(n) = 720*a(n-1) - 84448*a(n-2) + 1503360*a(n-3) - 17912224*a(n-4) - 318223104*a(n-5) + 564996096*a(n-6) + 270471168*a(n-7) - 11373824*a(n-8) + 65536*a(n-9).

Empirical g.f.: x*(1 - 588*x + 38508*x^2 - 610624*x^3 - 20571792*x^4 + 98269760*x^5 + 112896832*x^6 - 6488576*x^7 + 57344*x^8) / ((1 - 2*x)*(1 - 26*x + 512*x^2)*(1 - 114*x - 1156*x^2 + 8*x^3)*(1 - 578*x - 228*x^2 + 8*x^3)). - Colin Barker, Feb 27 2018

EXAMPLE

Some solutions for 4 X 7:

..1..2..3..4..5..6..7....1..2..3..4..5..7.10....1..2..3..4..5..7.10

..8..9.10.11.12.13.14....6..8..9.12.13.15.19....6..8..9.12.13.15.19

.15.16.17.18.19.20.21...11.14.17.18.20.22.24...11.14.17.18.20.22.25

.22.23.24.25.26.27.28...16.21.23.25.26.27.28...16.21.23.24.26.27.28

CROSSREFS

Cf. A181196.

Sequence in context: A146522 A183500 A146545 * A227596 A267951 A268098

Adjacent sequences:  A181191 A181192 A181193 * A181195 A181196 A181197

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 10 2010

STATUS

approved

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Last modified June 18 11:58 EDT 2021. Contains 345098 sequences. (Running on oeis4.)