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 A295270 #11 Oct 21 2023 09:46:07 %S A295270 7,33,164,811,4035,19997,99245,492401,2443097,12121712,60143345, %T A295270 298407987,1480586061,7346099129,36448521869,180843564461, %U A295270 897276298340,4451940313371,22088817679653,109596228179271,543774384192739 %N A295270 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s. %C A295270 Column 3 of A295275. %H A295270 R. H. Hardin, <a href="/A295270/b295270.txt">Table of n, a(n) for n = 1..210</a> %H A295270 Robert Israel, <a href="/A295270/a295270.pdf">Maple-assisted proof of formula</a> %H A295270 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2, 10, 20, 17, -1, -9, -12, -1, -1, 1). %F A295270 Empirical: a(n) = 2*a(n-1) + 10*a(n-2) + 20*a(n-3) + 17*a(n-4) - a(n-5) - 9*a(n-6) - 12*a(n-7) - a(n-8) - a(n-9) + a(n-10). %F A295270 Empirical formula is true: see link. - _Robert Israel_, Nov 19 2017 %e A295270 Some solutions for n=7: %e A295270 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 %e A295270 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 %e A295270 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 %e A295270 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 %e A295270 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 %e A295270 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 %e A295270 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 %Y A295270 Cf. A295275. %K A295270 nonn %O A295270 1,1 %A A295270 _R. H. Hardin_, Nov 19 2017