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 A083076 #16 Sep 08 2022 08:45:10
%S A083076 1,5,33,229,1601,11205,78433,549029,3843201,26902405,188316833,
%T A083076 1318217829,9227524801,64592673605,452148715233,3165041006629,
%U A083076 22155287046401,155087009324805,1085609065273633,7599263456915429,53194844198408001
%N A083076 Third row of number array A083075.
%C A083076 Binomial transform of A067411. Inverse binomial transform of A082412.
%C A083076 Trinomial transform of Jacobsthal numbers A001045. - _Paul Barry_, Sep 10 2007
%H A083076 Nathaniel Johnston, <a href="/A083076/b083076.txt">Table of n, a(n) for n = 0..250</a>
%H A083076 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F A083076 a(n) = (2*7^n + 1)/3.
%F A083076 G.f.: (1-3*x)/((1-x)*(1-7*x)).
%F A083076 E.g.f.: (2*exp(7*x) + exp(x))/3.
%F A083076 a(n) = Sum_{k=0..2*n} trinomial(n,k)*Fibonacci(k+1), where trinomial(n,k) are the trinomial coefficients (A027907). - _Paul Barry_, Sep 10 2007
%F A083076 a(n) = 7*a(n-1) - 2, a(n) = 8*a(n-1) - 7*a(n-2). - _Vincenzo Librandi_, Nov 06 2011
%p A083076 seq((2*7^n+1)/3,n=0..20); # _Nathaniel Johnston_, Jun 26 2011
%o A083076 (Magma) [(2*7^n+1)/3: n in [0..30]]; // _Vincenzo Librandi_, Nov 06 2011
%Y A083076 Cf. A034478, A066443, A082761, A083077.
%K A083076 nonn,easy
%O A083076 0,2
%A A083076 _Paul Barry_, Apr 23 2003