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 A174929 #9 Sep 08 2022 08:45:51 %S A174929 1,66,132,262,393,588,784,1044,1305,1630,1956,2346,2737,3192,3648, %T A174929 4168,4689,5274,5860,6510,7161,7876,8592,9372,10153,10998,11844,12754, %U A174929 13665,14640,15616,16656,17697,18802,19908,21078,22249,23484,24720,26020 %N A174929 Partial sums of A174928. %H A174929 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -2, 1). %F A174929 a(n) = (71+264*n+130*n^2-63*(-1)^n)/8. %F A174929 a(n) = a(n-1)+a(n-2)-a(n-3)+65 for n > 2; a(0) = 1, a(1) = 66, a(2) = 132. %F A174929 G.f.: (1+64*x)/((1-x)^3*(1+x)). %t A174929 LinearRecurrence[{2,0,-2,1},{1,66,132,262},60] (* _Harvey P. Dale_, Jul 12 2021 *) %o A174929 (Magma) T:=&cat[ [1, 64]: n in [0..19] ]; U:=[ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T] ]; [ n eq 1 select U[1] else Self(n-1)+U[n]: n in [1..#U] ]; %o A174929 [ n eq 1 select 1 else n le 3 select 66*(n-1) else Self(n-1)+Self(n-2)-Self(n-3)+65: n in [1..40] ]; %Y A174929 Cf. A174928 (partial sums of A174927), A174927 (repeat 1, 64). %K A174929 nonn %O A174929 0,2 %A A174929 _Klaus Brockhaus_, Apr 02 2010