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A250414 Number of length n+1 0..3 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

%I A250414 #6 Jul 23 2025 12:22:49
%S A250414 7,36,99,476,1693,7504,29221,123242,492076,2021436,8111306,32877666,
%T A250414 131905733,531080990,2128576994,8541648896,34206851593,137042168870,
%U A250414 548526597108,2195788650322,8786230110165,35158099104398,140658315422311
%N A250414 Number of length n+1 0..3 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.
%C A250414 Column 3 of A250419
%H A250414 R. H. Hardin, <a href="/A250414/b250414.txt">Table of n, a(n) for n = 1..210</a>
%F A250414 Empirical: a(n) = 12*a(n-1) -23*a(n-2) -252*a(n-3) +1056*a(n-4) +1766*a(n-5) -14214*a(n-6) -1040*a(n-7) +103693*a(n-8) -58064*a(n-9) -484016*a(n-10) +411280*a(n-11) +1566651*a(n-12) -1472256*a(n-13) -3670072*a(n-14) +3223960*a(n-15) +6306524*a(n-16) -4463544*a(n-17) -7823016*a(n-18) +3799616*a(n-19) +6723120*a(n-20) -1817056*a(n-21) -3791856*a(n-22) +352032*a(n-23) +1315312*a(n-24) +57408*a(n-25) -252160*a(n-26) -37120*a(n-27) +20352*a(n-28) +4608*a(n-29)
%e A250414 Some solutions for n=6
%e A250414 ..2....2....1....3....2....3....2....3....0....1....3....0....1....2....0....1
%e A250414 ..1....0....3....2....1....0....3....2....1....1....2....0....2....2....2....1
%e A250414 ..3....2....3....0....1....1....1....3....3....3....0....1....3....0....1....1
%e A250414 ..1....0....0....0....3....0....3....3....1....1....0....3....2....1....2....2
%e A250414 ..0....2....2....0....2....0....0....3....1....1....3....1....1....2....2....0
%e A250414 ..1....0....1....2....3....0....3....2....2....0....1....0....2....1....3....1
%e A250414 ..2....3....1....2....1....1....0....0....2....0....3....3....1....0....2....2
%K A250414 nonn
%O A250414 1,1
%A A250414 _R. H. Hardin_, Nov 22 2014