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 A263614 #11 Oct 26 2015 10:39:25 %S A263614 0,0,1,2,2,4,4,8,8,16,15,30,26,52,42,84,64,128,93,186,130,260,176,352, %T A263614 232,464,299,598,378,756,470,940,576,1152,697,1394,834,1668,988,1976, %U A263614 1160,2320,1351,2702,1562,3124,1794,3588,2048,4096,2325,4650,2626,5252,2952,5904,3304,6608,3683,7366 %N A263614 a(2n) = A000125(n), a(2n+1) = 2*a(2n). %C A263614 For n >= 2, number of palindromic squares of length n whose decimal digits are 0 or 1 and with 9 or fewer 1's. %H A263614 Colin Barker, <a href="/A263614/b263614.txt">Table of n, a(n) for n = 0..1000</a> %H A263614 G. J. Simmons, <a href="/A002778/a002778_2.pdf">Palindromic powers</a>, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] %H A263614 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1). %F A263614 From _Colin Barker_, Oct 26 2015: (Start) %F A263614 a(n) = (-((-1)^n*(-78+62*n-12*n^2+n^3))+3*(-26+42*n-8*n^2+n^3))/96. %F A263614 a(n) = 4*a(n-2)-6*a(n-4)+4*a(n-6)-a(n-8) for n>7. %F A263614 G.f.: x^2*(2*x+1)*(2*x^4-2*x^2+1) / ((x-1)^4*(x+1)^4). %F A263614 (End) %o A263614 (PARI) a(n) = (-((-1)^n*(-78+62*n-12*n^2+n^3))+3*(-26+42*n-8*n^2+n^3))/96 \\ _Colin Barker_, Oct 26 2015 %o A263614 (PARI) concat(vector(2), Vec(x^2*(2*x+1)*(2*x^4-2*x^2+1)/((x-1)^4*(x+1)^4) + O(x^100))) \\ _Colin Barker_, Oct 26 2015 %Y A263614 Cf. A000125, A263615. %K A263614 nonn,base,easy %O A263614 0,4 %A A263614 _N. J. A. Sloane_, Oct 23 2015