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 A269413 #8 Jan 21 2019 12:25:20 %S A269413 20,957,10132,56890,223320,695135,1837752,4302612,9168780,18124865, %T A269413 33696300,59523022,100692592,164133795,259075760,397577640,595133892, %U A269413 871360197,1250765060,1763612130,2446878280,3345312487,4512600552 %N A269413 Number of length-7 0..n arrays with no repeated value greater than or equal to the previous repeated value. %H A269413 R. H. Hardin, <a href="/A269413/b269413.txt">Table of n, a(n) for n = 1..210</a> %F A269413 Empirical: a(n) = n^7 + 7*n^6 + 11*n^5 + (8/3)*n^4 - (11/6)*n^3 + (1/3)*n^2 - (1/6)*n. %F A269413 Conjectures from _Colin Barker_, Jan 21 2019: (Start) %F A269413 G.f.: x*(20 + 797*x + 3036*x^2 + 1510*x^3 - 296*x^4 - 27*x^5) / (1 - x)^8. %F A269413 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8. %F A269413 (End) %e A269413 Some solutions for n=4: %e A269413 ..2. .3. .1. .2. .4. .1. .4. .0. .2. .2. .0. .1. .0. .3. .4. .0 %e A269413 ..2. .4. .2. .3. .4. .3. .1. .4. .3. .3. .3. .0. .2. .0. .4. .0 %e A269413 ..1. .1. .1. .0. .3. .0. .2. .2. .4. .0. .3. .1. .3. .1. .1. .4 %e A269413 ..2. .3. .3. .3. .3. .0. .4. .1. .4. .1. .2. .1. .2. .4. .4. .0 %e A269413 ..3. .4. .4. .3. .0. .3. .0. .2. .2. .2. .0. .0. .0. .2. .0. .4 %e A269413 ..1. .0. .1. .2. .2. .2. .2. .0. .4. .4. .3. .0. .2. .0. .4. .1 %e A269413 ..0. .4. .1. .0. .4. .1. .1. .1. .1. .0. .0. .1. .4. .2. .3. .3 %Y A269413 Row 7 of A269409. %K A269413 nonn %O A269413 1,1 %A A269413 _R. H. Hardin_, Feb 25 2016