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 A162899 #10 Sep 26 2020 12:55:13 %S A162899 1,10,14,30,39,64,80,116,141,190,226,290,339,420,484,584,665,786,886, %T A162899 1030,1151,1320,1464,1660,1829,2054,2250,2506,2731,3020,3276,3600, %U A162899 3889,4250,4574,4974,5335,5776,6176,6660,7101,7630,8114,8690,9219,9844,10420 %N A162899 Partial sums of [A052938(n)^2]. %C A162899 Another plausible solution, besides A115391 and A116955, to A115603: Each additional term of the partial sums here is the square of a number that alternately differs +2, -1, +2, -1, ..., from the previous number that is squared: a(3) = 30 = 1^2 + 3^2 + 2^2 + 4^2, where 1, 3, 2, 4 display this pattern. %H A162899 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1). %F A162899 a(n) = sum(k=0..n, A052938(n)^2). %F A162899 a(n) = (60-36*(-1)^n+(109-9*(-1)^n)*n+24*n^2+2*n^3)/24. G.f.: (4*x^4-4*x^3-7*x^2+8*x+1) / ((x-1)^4*(x+1)^2). - _Colin Barker_, Jul 18 2013 %t A162899 LinearRecurrence[{2,1,-4,1,2,-1},{1,10,14,30,39,64},50] (* _Harvey P. Dale_, Sep 26 2020 *) %o A162899 (PARI) a(n) = sum(k=0, n, (if(k%2==0, k+2, k+5)/2)^2) %Y A162899 Cf. A115603, A115391, A116955. %K A162899 nonn,easy %O A162899 0,2 %A A162899 _Rick L. Shepherd_, Jul 16 2009