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 A191584 #7 Feb 23 2023 14:14:27
%S A191584 1,0,4,1,14,6,47,26,154,99,496,352,1577,1200,4964,3977,15502,12918,
%T A191584 48103,41338,148490,130779,456416,410048,1397905,1276512,4268740,
%U A191584 3950929,13002638,12170598,39522143,37343834,119912698,114209811,363262672,348332320,1099015481,1059927312
%N A191584 Diagonal sums of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).
%H A191584 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-3).
%F A191584 a(n) = 3^(floor(n/2)+1)-fibonacci(n+3).
%F A191584 Recurrence: a(n+4)=a(n+3)+4*a(n+2)-3*a(n+1)-3*a(n).
%F A191584 G.f.: (1-x)/(1-x-4x^2+3x^3+3x^4) = (1-x)/((1-x-x^2)(1-3x^2)).
%t A191584 Table[3^(Floor[n/2]+1)-Fibonacci[n+3],{n,0,100}]
%t A191584 LinearRecurrence[{1,4,-3,-3},{1,0,4,1},40] (* _Harvey P. Dale_, Feb 23 2023 *)
%o A191584 (Maxima) makelist(3^(floor(n/2)+1)-fib(n+3),n,0,12);
%Y A191584 A191582.
%K A191584 nonn,easy
%O A191584 0,3
%A A191584 _Emanuele Munarini_, Jun 07 2011