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 A362067 #24 Jun 10 2024 08:52:01
%S A362067 0,2,6,18,50,136,364,966,2550,6710,17622,46224,121160,317434,831430,
%T A362067 2177322,5701290,14927768,39083988,102327390,267903350,701391022,
%U A362067 1836283246,4807480608,12586194000,32951158706,86267374854,225851115906,591286215650,1548007923880
%N A362067 Sum of successive Fibonacci numbers F(n) : a(n) = Sum_{k = 0..n} F(n+k).
%H A362067 Paolo Xausa, <a href="/A362067/b362067.txt">Table of n, a(n) for n = 0..1000</a>
%H A362067 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-2,1).
%F A362067 a(n) = 4*a(n-1)-3*a(n-2)-2*a(n-3)+a(n-4), a(0)=0, a(1)=2, a(2)=6, a(3)=18.
%F A362067 G.f.: 2*x*(1-x)/((1-3*x+x^2)*(1-x-x^2)).
%F A362067 a(n) = A000045(2n+2) - A000045(n+1).
%F A362067 a(n) = 2 * A094292(n+1). - _Alois P. Heinz_, Apr 07 2023
%F A362067 a(n) = A000045(n+1)*(A000032(n+1) - 1). - _Paolo Xausa_, Jun 10 2024
%e A362067 a(n) are the row sums of the triangle T(n,k) (A199334):
%e A362067 0;
%e A362067 1, 1;
%e A362067 1, 2, 3;
%e A362067 2, 3, 5, 8;
%e A362067 3, 5, 8, 13, 21;
%e A362067 5, 8, 13, 21, 34, 55;
%e A362067 ...
%e A362067 T(n,k) = T(n,k-1) + T(n-1, k-1); T(n,0) = A000045(n).
%t A362067 A362067[n_] := Fibonacci[n+1]*(LucasL[n+1] - 1); Array[A362067, 50, 0] (* or *)
%t A362067 LinearRecurrence[{4, -3, -2, 1}, {0, 2, 6, 18}, 50] (* _Paolo Xausa_, Jun 10 2024 *)
%Y A362067 Cf. A000032, A000045, A094292, A199334.
%K A362067 nonn,easy
%O A362067 0,2
%A A362067 _Philippe Deléham_, Apr 07 2023