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A264880 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,1 0,-1 -2,0 or 1,1.

%I A264880 #4 Nov 27 2015 07:36:28
%S A264880 1,0,5,4,65,228,1101,4832,18501,79088,306617,1273740,5039669,20532112,
%T A264880 82109789,331870404,1333905993,5375261200,21637089445,87118807544,
%U A264880 350809834405,1412328072196,5687276800137,22897079312012,92199483148325
%N A264880 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,1 0,-1 -2,0 or 1,1.
%C A264880 Row 3 of A264878.
%H A264880 R. H. Hardin, <a href="/A264880/b264880.txt">Table of n, a(n) for n = 1..210</a>
%F A264880 Empirical: a(n) = 4*a(n-1) +15*a(n-2) -68*a(n-3) -69*a(n-4) +516*a(n-5) -5*a(n-6) -2512*a(n-7) +1593*a(n-8) +11468*a(n-9) -15799*a(n-10) -49100*a(n-11) +101093*a(n-12) +164044*a(n-13) -436187*a(n-14) -389856*a(n-15) +1321846*a(n-16) +642184*a(n-17) -2924570*a(n-18) -715336*a(n-19) +4872606*a(n-20) +473736*a(n-21) -6251634*a(n-22) +6251634*a(n-24) -473736*a(n-25) -4872606*a(n-26) +715336*a(n-27) +2924570*a(n-28) -642184*a(n-29) -1321846*a(n-30) +389856*a(n-31) +436187*a(n-32) -164044*a(n-33) -101093*a(n-34) +49100*a(n-35) +15799*a(n-36) -11468*a(n-37) -1593*a(n-38) +2512*a(n-39) +5*a(n-40) -516*a(n-41) +69*a(n-42) +68*a(n-43) -15*a(n-44) -4*a(n-45) +a(n-46)
%e A264880 All solutions for n=4
%e A264880 .10..2.12..4.14...10..2..3..4.14....1..2.12..4.14....1..2..3..4.14
%e A264880 .15..0..1..9..3...15..0..1..9.19...15..0.17..9..3...15..0.17..9.19
%e A264880 .11..5..6..7..8...11..5..6..7..8...11..5..6..7..8...11..5..6..7..8
%e A264880 .16.17.18.19.13...16.17.18.12.13...16.10.18.19.13...16.10.18.12.13
%Y A264880 Cf. A264878.
%K A264880 nonn
%O A264880 1,3
%A A264880 _R. H. Hardin_, Nov 27 2015