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 A364636 #14 Jul 31 2023 08:06:28 %S A364636 0,1,6,21,68,205,594,1673,4616,12537,33630,89309,235212,615173, %T A364636 1599402,4137105,10653712,27327857,69856182,178017061,452390740, %U A364636 1146776253,2900399106,7320463897,18441561624,46376946025,116442406158,291929022189,730881930716,1827523107829 %N A364636 a(n) = ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n/2. %H A364636 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-4,-1). %F A364636 The sequence can be continued to all ZZ, and a(-n) = -(-1)^n*a(n). %F A364636 a(n) = [x^n] (x + 2*x^2 - x^3)/(-1 + x*(2 + x))^2. %F A364636 a(n) = 2*A364553(n) - A093967(n). %p A364636 A364636 := n -> ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n / 2: %p A364636 seq(simplify(A364636(n)), n = 0..29); %o A364636 (PARI) a(n) = ((1 - quadgen(8))^n + (1 + quadgen(8))^n)*n/2; \\ _Michel Marcus_, Jul 31 2023 %Y A364636 Cf. A093967, A364553. %K A364636 nonn,easy %O A364636 0,3 %A A364636 _Peter Luschny_, Jul 30 2023