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 A298034 #31 Jan 25 2018 06:49:39 %S A298034 1,7,19,43,73,115,163,223,289,367,451,547,649,763,883,1015,1153,1303, %T A298034 1459,1627,1801,1987,2179,2383,2593,2815,3043,3283,3529,3787,4051, %U A298034 4327,4609,4903,5203,5515,5833,6163,6499,6847,7201,7567,7939,8323,8713,9115,9523,9943,10369,10807,11251,11707 %N A298034 Partial sums of A298033. %H A298034 Colin Barker, <a href="/A298034/b298034.txt">Table of n, a(n) for n = 0..1000</a> %H A298034 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1). %F A298034 G.f.: (1 + 5*x + 5*x^2 + 7*x^3) / ((1 - x)^3*(1 + x)). %F A298034 From _Colin Barker_, Jan 25 2018: (Start) %F A298034 a(n) = (9*n^2 + 2) / 2 for n even. %F A298034 a(n) = (9*n^2 + 5) / 2 for n odd. %F A298034 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>3. (End) %F A298034 a(4*k+r) = 36*k*(2*k + r) + a(r) for r = 0..3. Example: if n=29 then k=7 and r=1, hence a(29) = 36*7*(2*7 + 1) + 7 = 3787. - _Bruno Berselli_, Jan 25 2018 %o A298034 (PARI) Vec((1 + 5*x + 5*x^2 + 7*x^3) / ((1 - x)^3*(1 + x)) + O(x^50)) \\ _Colin Barker_, Jan 25 2018 %Y A298034 Cf. A298033. %K A298034 nonn,easy %O A298034 0,2 %A A298034 _N. J. A. Sloane_, Jan 21 2018, corrected Jan 24 2018