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%I #13 Dec 10 2016 17:02:22
%S 0,1,0,25,0,289,0,2025,0,16641,0,145161,0,1185921,0,9715689,0,
%T 80874049,0,668377609,0,5516478529,0,45630513769,0,377252695681,0,
%U 3117897783049,0,25774558228225,0,213069752354281,0,1761278190732225,0,14559352270703881
%N Number of n X 4 arrays with every diagonal and antidiagonal of length L containing a permutation of 1..L.
%H R. H. Hardin, <a href="/A179809/b179809.txt">Table of n, a(n) for n=4..99</a>
%F a(n) = 4*a(n-2) +21*a(n-4) +150*a(n-6) -79*a(n-8) -1032*a(n-10) -4973*a(n-12) +5438*a(n-14) +5192*a(n-16) +39568*a(n-18) -54912*a(n-20) +34816*a(n-22) -220800*a(n-24) +362752*a(n-26) -301824*a(n-28) +811520*a(n-30) -536576*a(n-32) +581632*a(n-34) -1638400*a(n-36) -131072*a(n-38) -1048576*a(n-40) +2097152*a(n-42).
%F G.f.: -x^5* (1 +21*x^2 +168*x^4 +194*x^6 -1199*x^8 -4271*x^10 +5670*x^12 +4584*x^14 +33296*x^16 -65600*x^18 +62592*x^20 -246656*x^22 +485376*x^24 -470272*x^26 +946688*x^28 -806912*x^30 +679936*x^32 -1900544*x^34 +393216*x^36 -1048576*x^38 +2097152*x^40) / ( (x-1) *(1+x) *(2*x^2-1) *(2*x^2+x+1) *(2*x^2-x+1) *(2*x^3+x+1) *(2*x^3+x-1) *(4*x^3+2*x^2+1) *(4*x^3-2*x^2-1) *(4*x^3-4*x^2+x+1) *(4*x^3+4*x^2+x-1) *(128*x^12 -64*x^10 +40*x^8 -28*x^6 +14*x^4 +x^2 +1) *(2*x^4+x^2+1) ).
%e Some solutions for 7 X 4:
%e .1.2.1.1...1.2.2.1...1.1.2.1...1.2.2.1...1.1.1.1...1.2.2.1...1.2.1.1...1.1.1.1
%e .1.3.3.2...1.3.3.1...2.3.2.1...1.3.3.1...2.3.2.2...1.3.3.1...1.2.3.2...2.2.2.2
%e .2.4.4.1...1.2.4.1...1.4.2.3...1.2.2.1...2.3.4.3...1.4.2.1...3.4.3.1...3.3.3.3
%e .2.3.3.2...4.3.4.2...3.4.1.4...4.4.4.4...4.3.4.2...2.4.3.4...2.4.3.4...4.4.4.4
%e .1.4.4.2...2.3.4.3...3.4.3.3...3.3.3.3...1.2.4.1...3.4.3.2...1.4.2.2...1.2.2.1
%e .2.3.3.1...2.3.2.2...2.2.2.2...2.2.2.2...1.3.3.1...2.2.3.2...2.3.3.1...1.3.3.1
%e .1.1.2.1...1.1.1.1...1.1.1.1...1.1.1.1...1.2.2.1...1.1.1.1...1.1.2.1...1.2.2.1
%K nonn
%O 4,4
%A _R. H. Hardin_, formula from _Alois P. Heinz_ and _R. J. Mathar_ in the Sequence Fans Mailing List, Jul 28 2010
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