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 A269607 #8 Jan 25 2019 08:28:57 %S A269607 8,62,222,572,1220,2298,3962,6392,9792,14390,20438,28212,38012,50162, %T A269607 65010,82928,104312,129582,159182,193580,233268,278762,330602,389352, %U A269607 455600,529958,613062,705572,808172,921570,1046498,1183712,1333992 %N A269607 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by one or less. %H A269607 R. H. Hardin, <a href="/A269607/b269607.txt">Table of n, a(n) for n = 1..210</a> %F A269607 Empirical: a(n) = n^4 + 4*n^3 + 4*n^2 - n. %F A269607 Conjectures from _Colin Barker_, Jan 25 2019: (Start) %F A269607 G.f.: 2*x*(4 + 11*x - 4*x^2 + x^3) / (1 - x)^5. %F A269607 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. %F A269607 (End) %e A269607 Some solutions for n=7: %e A269607 ..0. .7. .6. .5. .4. .1. .1. .5. .3. .5. .0. .3. .1. .3. .4. .4 %e A269607 ..5. .6. .4. .1. .0. .2. .4. .1. .4. .1. .3. .0. .7. .0. .6. .3 %e A269607 ..3. .5. .6. .7. .6. .1. .6. .7. .3. .7. .4. .3. .0. .6. .0. .7 %e A269607 ..7. .7. .6. .5. .1. .4. .2. .4. .2. .6. .7. .4. .1. .7. .1. .7 %Y A269607 Row 4 of A269606. %K A269607 nonn %O A269607 1,1 %A A269607 _R. H. Hardin_, Mar 01 2016