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 A338225 #37 Jan 11 2022 05:49:38 %S A338225 2,11,23,66,167,443,1154,3027,7919,20738,54287,142131,372098,974171, %T A338225 2550407,6677058,17480759,45765227,119814914,313679523,821223647, %U A338225 2149991426,5628750623,14736260451,38580030722,101003831723,264431464439,692290561602,1812440220359,4745030099483 %N A338225 a(n) = F(n+3) * F(n+1) + (-1)^n where F(n) = A000045(n) are the Fibonacci numbers. %C A338225 Twice the difference between the areas of consecutive deltoids with cross lengths F(n+3) and F(n). %C A338225 Also it is the difference between the areas of consecutive rectangles with side lengths F(n+3) and F(n). %C A338225 Also first differences of A226205 for n > 2. %D A338225 Burak Muslu, Sayılar ve Bağlantılar, Luna, 2021, p. 50. %H A338225 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1). %F A338225 a(n) = F(n+3) * F(n+1) + (-1)^n, for n > 0. %F A338225 G.f.: x*(2 + 7*x - 3*x^2)/(1 - 2*x - 2*x^2 + x^3). - _Stefano Spezia_, Jan 30 2021 %F A338225 a(n) = F(n+2)^2 + 2*(-1)^n = A007598(n+2) + 2*(-1)^n. - _Amiram Eldar_, Jan 11 2022 %e A338225 For n = 2, a(2) = F(2+3) * F(2+1) + (-1)^2 = 5 * 2 + 1 = 11. %t A338225 a[n_] := Fibonacci[n + 3] * Fibonacci[n + 1] + (-1)^n; Array[a, 30] (* _Amiram Eldar_, Jan 30 2021 *) %o A338225 (PARI) a(n) = fibonacci(n+3)*fibonacci(n+1) + (-1)^n; \\ _Michel Marcus_, Mar 25 2021 %Y A338225 Cf. A000045, A007598, A226205, A341208. %K A338225 nonn,easy %O A338225 1,1 %A A338225 _Burak Muslu_, Jan 30 2021