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 A213299 #19 Feb 08 2023 12:38:47 %S A213299 2,5,10,17,40,77,130,203,440,813,1350,2087,4460,8197,13570,20943, %T A213299 44680,82053,135790,209527,446900,820637,1358010,2095383,4469120, %U A213299 8206493,13580230,20953967,44691340 %N A213299 Partial sums of A211681. %C A213299 The terms are primes for n = 1, 2, 4, 12, 22, 32 and possibly further n’s (Question). %H A213299 Hieronymus Fischer, <a href="/A213299/b213299.txt">Table of n, a(n) for n = 1..100</a> %H A213299 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,9,-18,9,0,10,-20,10). %F A213299 a(n) = ((3982 + 2709*k + 567*k^2 + 54*k^3)*10^m - 1980*m - 2200 - 495*k + 162*((n+1) mod 2) * (-1)^m * (-1)^floor(n/2))/891, where m=floor((n-1)/4), k=(n-1) mod 4. %F A213299 G.f.: (2*x*(1+x^10) + 3*x^2*(1 + x^3 + x^5 + x^6) + 5*x^3*(1+x^6) + 7*x^4*(1+x^2))/((1-x)*(1-10*x^4)*(1-x^8)). %F A213299 From _Chai Wah Wu_, Feb 08 2023: (Start) %F A213299 a(n) = 2*a(n-1) - a(n-2) + 9*a(n-4) - 18*a(n-5) + 9*a(n-6) + 10*a(n-8) - 20*a(n-9) + 10*a(n-10) for n > 10. %F A213299 G.f.: x*(-2*x^7 + 2*x^6 - 5*x^5 + 2*x^4 - 2*x^3 - 2*x^2 - x - 2)/((x - 1)^2*(x^4 + 1)*(10*x^4 - 1)). (End) %Y A213299 Cf. A019546, A035232, A039996, A046034, A085823, A211681, A211682. %K A213299 nonn,easy,base %O A213299 1,1 %A A213299 _Hieronymus Fischer_, Jun 08 2012 %E A213299 Typo in g.f. corrected by _Hieronymus Fischer_, Sep 03 2012