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A264374 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

%I A264374 #4 Nov 12 2015 07:56:34
%S A264374 4,6,80,441,3249,22484,156293,1097881,7657324,53631087,374971549,
%T A264374 2623479579,18351250984,128373536659,898014323096,6281872878413,
%U A264374 43943675806740,307399346962192,2150352679484064,15042375439676549
%N A264374 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.
%C A264374 Column 3 of A264379.
%H A264374 R. H. Hardin, <a href="/A264374/b264374.txt">Table of n, a(n) for n = 1..210</a>
%F A264374 Empirical: a(n) = 2*a(n-1) +58*a(n-2) -21*a(n-3) -1238*a(n-4) -137*a(n-5) +15288*a(n-6) +4560*a(n-7) -127006*a(n-8) -47282*a(n-9) +772066*a(n-10) +326725*a(n-11) -3602505*a(n-12) -1772071*a(n-13) +13317616*a(n-14) +7874851*a(n-15) -39927191*a(n-16) -28721785*a(n-17) +98667418*a(n-18) +85571362*a(n-19) -202707758*a(n-20) -208446136*a(n-21) +346194120*a(n-22) +417845725*a(n-23) -485816139*a(n-24) -693362865*a(n-25) +544797544*a(n-26) +951161517*a(n-27) -465400385*a(n-28) -1074696221*a(n-29) +273846246*a(n-30) +1005646712*a(n-31) -64145514*a(n-32) -794935940*a(n-33) -92496118*a(n-34) +530782727*a(n-35) +167673359*a(n-36) -287037779*a(n-37) -164313896*a(n-38) +113531703*a(n-39) +114897917*a(n-40) -21596495*a(n-41) -58034484*a(n-42) -7483588*a(n-43) +20885338*a(n-44) +8031702*a(n-45) -5392938*a(n-46) -3705501*a(n-47) +1026905*a(n-48) +1321563*a(n-49) -64616*a(n-50) -395895*a(n-51) -61769*a(n-52) +89081*a(n-53) +29582*a(n-54) -14918*a(n-55) -7198*a(n-56) +2444*a(n-57) +1572*a(n-58) -165*a(n-59) -174*a(n-60) +15*a(n-61) +14*a(n-62) -2*a(n-63) -a(n-64)
%e A264374 Some solutions for n=4
%e A264374 ..4..2..6..5....4..2..6..5....1..2..4..7....1..2..3..5....1..5..6..7
%e A264374 ..0..1.10..3....0..1..8.11....0..9.10..3....0..6..8..9....0..9..2..3
%e A264374 ..9.13.11..7....9..3.12.13...12..5..6.13....4.10.11..7....4.10.11.13
%e A264374 ..8.14.16.17...16..7.10.19....8.14.16.11...13.17.16.19....8.14.16.17
%e A264374 .12.18.19.15...17.18.14.15...17.18.19.15...12.18.14.15...12.18.19.15
%Y A264374 Cf. A264379.
%K A264374 nonn
%O A264374 1,1
%A A264374 _R. H. Hardin_, Nov 12 2015