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 A079862 #24 Nov 05 2020 13:26:12
%S A079862 18,38,80,168,352,736,1536,3200,6656,13824,28672,59392,122880,253952,
%T A079862 524288,1081344,2228224,4587520,9437184,19398656,39845888,81788928,
%U A079862 167772160,343932928,704643072,1442840576,2952790016,6039797760,12348030976,25232932864
%N A079862 a(i) = the number of occurrences of 9's in the palindromic compositions of n=2*i-1 = the number of occurrences of 10's in the palindromic compositions of n=2*i.
%C A079862 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 A079862 Colin Barker, <a href="/A079862/b079862.txt">Table of n, a(n) for n = 10..1000</a>
%H A079862 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 A079862 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A079862 a(n) = (n+8)*2^(n-10).
%F A079862 From _Colin Barker_, Sep 29 2015: (Start)
%F A079862 a(n) = 2*A159697(n-10).
%F A079862 a(n) = 4*a(n-1) - 4*a(n-2) for n>11.
%F A079862 G.f.: -2*x^10*(17*x-9) / (2*x-1)^2.
%F A079862 (End)
%e A079862 a(10) = 18 since the palindromic compositions of 19 that contain a 9 are 9+1+9 and the 16 compositions of the form c+9+(reverse of c), where c represents a composition of 5.
%t A079862 Table[(8 + i)*2^(i - 10), {i, 10, 50}]
%o A079862 (PARI) Vec(-2*x^10*(17*x-9)/(2*x-1)^2 + O(x^100)) \\ _Colin Barker_, Sep 29 2015
%Y A079862 Cf. A057711, A001792, A079859, A078836, A079861, A079863.
%K A079862 easy,nonn
%O A079862 10,1
%A A079862 Silvia Heubach (sheubac(AT)calstatela.edu), Jan 11 2003