This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A205306 #8 Jul 22 2025 18:46:34 %S A205306 12,2191,381958,70985206,13049279920,2404472055439,442834241887042, %T A205306 81565593153176155,15023237028425135528,2767081708267517685850, %U A205306 509659402434339115696776,93872456554136530629815555 %N A205306 Number of nX4 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order. %C A205306 Column 4 of A205310 %H A205306 R. H. Hardin, <a href="/A205306/b205306.txt">Table of n, a(n) for n = 1..210</a> %F A205306 Empirical: a(n) = 138*a(n-1) +9087*a(n-2) -80152*a(n-3) -5124946*a(n-4) +37705868*a(n-5) +99346827*a(n-6) +17722141556*a(n-7) -261185384994*a(n-8) +714699066626*a(n-9) -15202912141613*a(n-10) +304934550079298*a(n-11) -1225389716322737*a(n-12) -933781202067468*a(n-13) -33805706864300454*a(n-14) +185474258286271178*a(n-15) +1505623972530492162*a(n-16) -5117407741799018012*a(n-17) -25380195891304445642*a(n-18) +36229117914918274800*a(n-19) +251716664318924304110*a(n-20) -57605851368069887202*a(n-21) -1572473827570790923150*a(n-22) +3125955801166175823856*a(n-23) +17062517535287193726997*a(n-24) -32422586388875348507390*a(n-25) -159910400746542325205407*a(n-26) +54332608228198865319136*a(n-27) +661022488412915752154803*a(n-28) -721321139998771867284976*a(n-29) -3898866024012351846512850*a(n-30) +8412783886991366949353912*a(n-31) +30366027249263904221568708*a(n-32) -31118625776087432549655374*a(n-33) -111729795190877573537105846*a(n-34) +173816789359823529339671964*a(n-35) +553846546751160710968339655*a(n-36) -491036374242582108130054650*a(n-37) -2388488759973180614259754299*a(n-38) +22872473135117365385257812*a(n-39) +3637708187356950277191989337*a(n-40) -5888644440469728116298052320*a(n-41) -11635513023181409403942859614*a(n-42) +21091653515446386649943887296*a(n-43) +46583550442447069247305690806*a(n-44) -12430137563792000600050770102*a(n-45) -75388261189276904319964385046*a(n-46) +5063083350236789682463303536*a(n-47) +82424407966823722700175286140*a(n-48) -21774887291888889019777511748*a(n-49) -57879941791365958357832645088*a(n-50) +37727395614936350378426942136*a(n-51) +19448471990119789641851858295*a(n-52) -25295452552287517410871856028*a(n-53) -1750790964891024780004737837*a(n-54) +8054517038069608971655873284*a(n-55) +238128699519517099475692602*a(n-56) -2376060075223639793908923996*a(n-57) -401856855452402783889059865*a(n-58) +1146937237342456226969479554*a(n-59) +181659002124956734165606650*a(n-60) -391677684362411951192598594*a(n-61) -58125167210869815728999295*a(n-62) +77982926942952062273163618*a(n-63) -1014467950258371834786963*a(n-64) -13318075675102589346103236*a(n-65) -2967557913938184769133316*a(n-66) +12477808904841273824317728*a(n-67) +4694214069617141148458976*a(n-68) -6736162769502273391513536*a(n-69) -1685763587529755229146112*a(n-70) +1487182043605291803500544*a(n-71) +445045584055138381209600*a(n-72) -248152311461700801478656*a(n-73) -19790145808333878067200*a(n-74) +11874087485000326840320*a(n-75) %e A205306 Some solutions for n=5 %e A205306 ..0..1..0..2....0..0..1..0....0..0..1..2....0..0..1..0....0..0..1..1 %e A205306 ..0..3..3..0....0..2..1..3....0..2..2..1....0..0..1..2....1..0..2..1 %e A205306 ..1..3..2..1....2..0..2..0....1..0..1..1....1..1..2..3....0..1..0..2 %e A205306 ..1..2..1..1....2..0..1..2....2..2..1..0....1..3..3..1....2..1..0..3 %e A205306 ..0..2..0..3....1..3..0..0....0..3..0..0....2..3..0..1....1..0..1..0 %K A205306 nonn %O A205306 1,1 %A A205306 _R. H. Hardin_ Jan 25 2012