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 A258948 #18 Sep 08 2022 08:46:13
%S A258948 1,2,4,10,34,214,3886,419902,816293374,171382426877950,
%T A258948 69949169911638289022974,5994029248777394614754727872037912574,
%U A258948 209638685189029793998133268981457005889853767752082771673086
%N A258948 a(1)=1, a(2)=2; for n>2, a(n) = (1/2)*a(n-1)*a(n-2) + a(n-1) + a(n-2).
%C A258948 a(n) + 2 = (1/2)*(a(n-1) + 2)*(a(n-2) + 2), from which the general formula can be proved using the method shown in A063896.
%F A258948 a(n) = 2 * 3^A000045(n-2) * 2^A000045(n-3) - 2, where A000045(n) is the n-th Fibonacci number.
%e A258948 a(3) = (1/2)*2*1 + 2 + 1 = 4;
%e A258948 a(4) = (1/2)*4*2 + 4 + 2 = 10;
%e A258948 a(5) = (1/2)*10*4 + 10 + 4 = 34;
%e A258948 a(6) = 2*(3^3)(2^2) - 2 = 214.
%t A258948 Table[2 3^Fibonacci[n-2] 2^Fibonacci[n-3] - 2, {n, 1, 20}] (* _Vincenzo Librandi_, Jun 17 2015 *)
%o A258948 (Magma) [n le 2 select n else Self(n-1)*Self(n-2)/2+Self(n-1)+Self(n-2): n in [1..13]];
%o A258948 (PARI) a(n) = 2*(3^fibonacci(n-2))*(2^fibonacci(n-3)) - 2; \\ _Michel Marcus_, Jun 17 2015
%o A258948 (Magma) [2*3^Fibonacci(n-2)*2^Fibonacci(n-3)-2: n in [1..20]]; // _Vincenzo Librandi_, Jun 17 2015
%Y A258948 Cf. A000045, A063896, A100701, A254132.
%K A258948 nonn,easy
%O A258948 1,2
%A A258948 _Morris Neene_, Jun 15 2015