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 A232621 #29 Dec 08 2022 06:08:11 %S A232621 1,8,31,175,1015,5911,34447,200767,1170151,6820135,39750655,231683791, %T A232621 1350352087,7870428727,45872220271,267362892895,1558305137095, %U A232621 9082467929671,52936502440927,308536546715887,1798282777854391,10481160120410455,61088677944608335 %N A232621 The number of vertically fault-free domino tilings of the 5 X (2n) board. %C A232621 A003775 counts the tilings of the 5 X (2n) board, and this sequence here counts only those that cannot be broken into tilings of two or more smaller 5 X (2n') boards with edge lengths n' < n by cutting "vertically" through the tiling parallel to the "short" side of length 5. %C A232621 Technically speaking this is the inverse INVERT transform of A003775 (see the comment in A005178). %H A232621 Colin Barker, <a href="/A232621/b232621.txt">Table of n, a(n) for n = 0..1000</a> %H A232621 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1). %F A232621 G.f.: (1 + x - 18*x^2 + 13*x^3 - x^4)/((1-x)*(1 - 6*x + x^2)). %F A232621 a(n) = 1 + 6*A001653(n) for n>1. - _Bruno Berselli_, Nov 27 2013 %F A232621 a(n) = 6*a(n-1) - a(n-2) - 4, n>=4. - _R. J. Mathar_, Nov 07 2015 %F A232621 a(n) = 1 + (3/2)*(3-2*sqrt(2))^n*(2+sqrt(2)) + (3-3/sqrt(2))*(3+2*sqrt(2))^n for n>1. - _Colin Barker_, Mar 05 2016 %o A232621 (PARI) Vec((-18*x^2+13*x^3-x^4+x+1)/((1-x)*(1-6*x+x^2)) + O(x^30)) \\ _Colin Barker_, Mar 05 2016 %Y A232621 Cf. A003775, A068924. %K A232621 nonn,easy %O A232621 0,2 %A A232621 _R. J. Mathar_, Nov 27 2013