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A184477 T(n,k)=1/6 the number of (n+2)X(k+2) 0..2 arrays with each 3X3 subblock containing one of one value, four of another, and four of the last.

%I A184477 #7 Jul 22 2025 09:36:05
%S A184477 315,1095,1095,3705,2755,3705,12339,7085,7085,12339,45585,19119,14119,
%T A184477 19119,45585,161739,62213,30681,30681,62213,161739,559305,200215,
%U A184477 86575,53739,86575,200215,559305,2147931,645837,249953,127689,127689,249953
%N A184477 T(n,k)=1/6 the number of (n+2)X(k+2) 0..2 arrays with each 3X3 subblock containing one of one value, four of another, and four of the last.
%C A184477 Table starts
%C A184477 ......315.....1095.....3705....12339....45585..161739..559305.2147931..7836561
%C A184477 .....1095.....2755.....7085....19119....62213..200215..645837.2386807..8440325
%C A184477 .....3705.....7085....14119....30681....86575..249953..747735.2652785..9085231
%C A184477 ....12339....19119....30681....53739...127689..322275..878625.2967411..9800745
%C A184477 ....45585....62213....86575...127689...247879..520289.1219455.3727073.11454631
%C A184477 ...161739...200215...249953...322275...520289..904411.1782585.4808779.13539521
%C A184477 ...559305...645837...747735...878625..1219455.1782585.2909367
%C A184477 ..2147931..2386807..2652785..2967411..3727073.4808779
%C A184477 ..7836561..8440325..9085231..9800745.11454631
%C A184477 .27667251.29121087.30632409.32238603
%H A184477 R. H. Hardin, <a href="/A184477/b184477.txt">Table of n, a(n) for n = 1..97</a>
%F A184477 Empirical for columns 3 to at least 4: a(n)=6*a(n-1)-11*a(n-2)+129*a(n-3)-738*a(n-4)+1353*a(n-5)-6290*a(n-6)+33312*a(n-7)-61072*a(n-8)+155640*a(n-9)-733968*a(n-10)+1345608*a(n-11)-2177568*a(n-12)+8661600*a(n-13)-15879600*a(n-14)+18027792*a(n-15)-56197152*a(n-16)+103028112*a(n-17)-89177760*a(n-18)+197883648*a(n-19)-362786688*a(n-20)+256296960*a(n-21)-350479872*a(n-22)+642546432*a(n-23)-390790656*a(n-24)+241864704*a(n-25)-443418624*a(n-26)+241864704*a(n-27)
%e A184477 Some solutions with a(1,1)=0 for 5X4
%e A184477 ..0..0..1..0....0..1..2..0....0..0..2..0....0..1..1..0....0..1..1..0
%e A184477 ..0..1..1..2....0..2..0..0....0..2..0..0....0..1..0..0....0..1..0..0
%e A184477 ..2..1..0..0....0..2..2..0....1..2..2..1....2..1..0..2....0..2..1..0
%e A184477 ..1..0..0..1....0..2..1..0....0..0..2..0....1..1..0..1....1..0..1..1
%e A184477 ..0..1..1..2....0..2..0..0....2..0..0..2....1..0..0..1....1..0..0..1
%K A184477 nonn,tabl
%O A184477 1,1
%A A184477 _R. H. Hardin_ Jan 15 2011