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A194778 T(n,k)=Number of lower triangles of an (n+2k-2)X(n+2k-2) 0..k array with new values introduced in row major order 0..k and no element unequal to more than one horizontal or vertical neighbor.

%I A194778 #7 Jul 22 2025 12:36:07
%S A194778 1,7,3,43,17,6,268,105,41,12,1740,672,265,95,23,11862,4490,1736,655,
%T A194778 219,43,85013,31466,11857,4464,1641,493,79,639760,231445,85007,31429,
%U A194778 11686,4069,1101,143,5045610,1784788,639753,231395,84727,30608,10121,2427,256
%N A194778 T(n,k)=Number of lower triangles of an (n+2k-2)X(n+2k-2) 0..k array with new values introduced in row major order 0..k and no element unequal to more than one horizontal or vertical neighbor.
%C A194778 Table starts
%C A194778 ...1....7....43....268....1740....11862.....85013.....639760....5045610
%C A194778 ...3...17...105....672....4490....31466....231445....1784788...14404218
%C A194778 ...6...41...265...1736...11857....85007....639753....5045602...41615156
%C A194778 ..12...95...655...4464...31429...231395...1784723...14404136..121420974
%C A194778 ..23..219..1641..11686...84727...639325...5044981...41614291..358184223
%C A194778 ..43..493..4069..30608..229869..1782111..14399939..121414559.1066897441
%C A194778 ..79.1101.10121..80961..631373..5029741..41587186..358138793.3210593393
%C A194778 .143.2427.25025.214469.1745459.14321783.121261490.1066617315
%H A194778 R. H. Hardin, <a href="/A194778/b194778.txt">Table of n, a(n) for n = 1..120</a>
%e A194778 Some solutions for n=2 k=2
%e A194778 ..0........0........0........0........0........0........0........0
%e A194778 ..0.0......0.0......1.1......1.1......0.0......1.1......0.1......0.0
%e A194778 ..1.1.1....0.0.1....1.1.2....1.1.1....0.0.0....1.1.1....0.1.1....0.0.0
%e A194778 ..1.1.1.0..0.0.1.1..1.1.2.2..0.0.0.0..0.0.0.1..2.2.2.2..0.1.1.0..1.1.1.1
%Y A194778 Column 1 is A055244
%K A194778 nonn,tabl
%O A194778 1,2
%A A194778 _R. H. Hardin_ Sep 02 2011