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 A302588 #86 Mar 04 2024 00:33:46
%S A302588 1,2,4,8,16,25,36,51,67,85,107,130,155,184,214,246,282,319,358,401,
%T A302588 445,491,541,592,645,702,760,820,884,949,1016,1087,1159,1233,1311,
%U A302588 1390,1471,1556,1642,1730,1822,1915,2010
%N A302588 a(n) = a(n-3) + 7*(n-2), a(0)=1, a(1)=2, a(2)=4.
%C A302588 Third of a family after A000124 and A084684. Built from the second differences. The fourth sequence is 1, 2, 4, 8, 16, 32, 49, 91, ..., from periodic [1, 2, 4, 8].
%D A302588 0
%H A302588 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 1, -2, 1).
%F A302588 Repeat the second differences of 1, 2, 4, 8, 16, i.e., repeat [1, 2, 4].
%F A302588 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).
%F A302588 a(n) = A069705(n) + 7*A130518(n).
%t A302588 CoefficientList[ Series[-(4x^4 +x^3 +x^2 +1)/((x -1)^3 (x^2 +x +1)), {x, 0, 50}], x] (* or *)
%t A302588 LinearRecurrence[{2, -1, 1, -2, 1}, {1, 2, 4, 8, 16}, 50] (* _Robert G. Wilson v_, Jul 18 2018 *)
%Y A302588 Cf. A069705, A047350 (first differences), A130518.
%K A302588 nonn
%O A302588 0,2
%A A302588 _Paul Curtz_, Jul 17 2018