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 A213586 #17 Sep 08 2022 08:46:02
%S A213586 1,6,20,51,112,224,421,758,1324,2263,3808,6336,10457,17158,28036,
%T A213586 45675,74256,120544,195485,316790,513116,830831,1344960,2176896,
%U A213586 3523057,5701254,9225716,14928483,24155824,39086048,63243733,102331766
%N A213586 Antidiagonal sums of the convolution array A213584.
%C A213586 a(n) is the number of bit strings of length n+5 with the pattern 01 at least thrice, and without the pattern 110, see example. - _John M. Campbell_, Jan 25 2013
%H A213586 Clark Kimberling, <a href="/A213586/b213586.txt">Table of n, a(n) for n = 1..500</a>
%H A213586 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,1,2,-1).
%F A213586 a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5).
%F A213586 G.f.: x*(1 + 2*x + x^2)/((1 - x - x^2)*(1 - x)^3).
%F A213586 a(n) = Fibonacci(n+8) - (21 + 10*n + 2*n^2). - _G. C. Greubel_, Jul 06 2019
%e A213586 From _John M. Campbell_, Jan 25 2013: (Start)
%e A213586 There are a(3) = 20 bit strings of length 3+5 with the pattern 01 at least thrice, and without the pattern 110:
%e A213586 00010101, 00100101, 00101001, 00101010, 00101011,
%e A213586 01000101, 01001001, 01001010, 01001011, 01010001,
%e A213586 01010010, 01010011, 01010100, 01010101, 01010111,
%e A213586 10010101, 10100101, 10101001, 10101010, 10101011.
%e A213586 (End)
%t A213586 (See A213584.)
%t A213586 With[{F = Fibonacci}, Table[F[n+8] -(21+10*n+2*n^2), {n,40}]] (* _G. C. Greubel_, Jul 06 2019 *)
%o A213586 (PARI) vector(40, n, fibonacci(n+8) -(21+10*n+2*n^2)) \\ _G. C. Greubel_, Jul 06 2019
%o A213586 (Magma) [Fibonacci(n+8) -(21+10*n+2*n^2): n in [1..40]]; // _G. C. Greubel_, Jul 06 2019
%o A213586 (Sage) [fibonacci(n+8) -(21+10*n+2*n^2) for n in (1..40)] # _G. C. Greubel_, Jul 06 2019
%o A213586 (GAP) List([1..40], n-> Fibonacci(n+8) -(21+10*n+2*n^2)) # _G. C. Greubel_, Jul 06 2019
%Y A213586 Cf. A213500, A213584, A213590.
%K A213586 nonn,easy
%O A213586 1,2
%A A213586 _Clark Kimberling_, Jun 18 2012