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 A079863 #20 Nov 05 2020 13:26:28
%S A079863 34,70,144,296,608,1248,2560,5248,10752,22016,45056,92160,188416,
%T A079863 385024,786432,1605632,3276800,6684672,13631488,27787264,56623104,
%U A079863 115343360,234881024,478150656,973078528,1979711488,4026531840,8187281408,16642998272,33822867456
%N A079863 a(n) is the number of occurrences of 11s in the palindromic compositions of m=2*n-1 = the number of occurrences of 12s in the palindromic compositions of m=2*n.
%C A079863 This sequence is part of a family of sequences, namely R(n,k), the number of ks in palindromic compositions of n. See also A057711, A001792, A078836, A079861, A079862. General formula: R(n,k)=2^(floor(n/2) - k) * (2 + floor(n/2) - k) if n and k have different parity and R(n,k)=2^(floor(n/2) - k) * (2 + floor(n/2) - k + 2^(floor((k+1)/2 - 1)) otherwise, for n >= 2k.
%H A079863 Colin Barker, <a href="/A079863/b079863.txt">Table of n, a(n) for n = 12..1000</a>
%H A079863 P. Chinn, R. Grimaldi and S. Heubach, <a href="https://www.calstatela.edu/sites/default/files/users/u1231/Papers/freqs.pdf">The frequency of summands of a particular size in Palindromic Compositions</a>, Ars Combin. 69 (2003), 65-78.
%H A079863 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A079863 a(n) = (n+22)*2^(n-12).
%F A079863 From _Colin Barker_, Sep 29 2015: (Start)
%F A079863 a(n) = 4*a(n-1) - 4*a(n-2) for n>13.
%F A079863 G.f.: -2*x^12*(33*x-17) / (2*x-1)^2.
%F A079863 (End)
%e A079863 a(12) = 34 since the palindromic compositions of 23 that contain a 11 are 11+1+11 and the 32 compositions of the form c+11+(reverse of c), where c represents a composition of 6.
%t A079863 Table[(22 + i)*2^(i - 12), {i, 12, 50}]
%t A079863 LinearRecurrence[{4,-4},{34,70},30] (* _Harvey P. Dale_, Jan 30 2017 *)
%o A079863 (PARI) Vec(-2*x^12*(33*x-17)/(2*x-1)^2 + O(x^100)) \\ _Colin Barker_, Sep 29 2015
%o A079863 (PARI) a(n)=(n+22)<<(n-12) \\ _Charles R Greathouse IV_, Sep 29 2015
%Y A079863 Cf. A057711, A001792, A079859, A078836, A079861, A079862.
%K A079863 easy,nonn
%O A079863 12,1
%A A079863 Silvia Heubach (sheubac(AT)calstatela.edu), Jan 11 2003