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 A059524 #33 Dec 18 2024 19:09:08 %S A059524 0,10,108,1126,11506,116166,1168586,11749134,118127408,1187692422, %T A059524 11941503498,120064335342,1207171430452,12137349489598, %U A059524 122033415224922,1226969238084836,12336404001299200,124034783402890620,1247091736942594618,12538723071673581562 %N A059524 Number of nonzero 4 X n binary arrays with all 1's connected. %C A059524 Old name was "Number of 4 X n checkerboards in which the set of red squares is edge connected". %C A059524 The number of connected (non-null) induced subgraphs in the grid graph P_4 X P_n. - _Andrew Howroyd_, May 20 2017 %H A059524 Andrew Howroyd, <a href="/A059524/b059524.txt">Table of n, a(n) for n = 0..200</a> %H A059524 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (17,-90,230,-272,-75,623,-632,65,255,-198,162,-96,11,1). %F A059524 Empirical g.f.: 2*x*(1 + x)*(5 - 36*x + 131*x^2 - 239*x^3 + 131*x^4 + 94*x^5 - 157*x^6 + 61*x^7 - 73*x^8 + 18*x^9 + x^10) / ((1 - x)^2*(1 - 15*x + 59*x^2 - 97*x^3 + 19*x^4 + 210*x^5 - 222*x^6 - 22*x^7 + 113*x^8 - 7*x^9 + 71*x^10 - 13*x^11 - x^12)). - _Colin Barker_, Oct 11 2017 %F A059524 The recurrence is correct. See A287151. - _Andrew Howroyd_, Dec 18 2024 %e A059524 a(1) = 10 because there are 4 positions to place a single 1, 3 ways to place a pair of adjacent 1's, 2 ways to place a triple of connected 1's, and 1 way for the all-1's array: 4+3+2+1=10. - _R. J. Mathar_, Mar 13 2023 %Y A059524 Row 4 of A287151. %Y A059524 Cf. A059020, A059021. %K A059524 nonn %O A059524 0,2 %A A059524 _David Radcliffe_, Jan 21 2001 %E A059524 Clearer name from _R. H. Hardin_, Jul 06 2009 %E A059524 a(16) corrected by _Andrew Howroyd_, May 20 2017