cp's OEIS Frontend

A026599 a(n) = Sum_{j=0..2*i, i=0..n} A026584(i,j).

%I A026599 #35 Jul 08 2022 13:03:26
%S A026599 1,3,9,23,61,155,401,1023,2629,6723,17241,44135,113101,289643,742049,
%T A026599 1900623,4868821,12471315,31946601,81831863,209618269,536945723,
%U A026599 1375418801,3523201695,9024876901,23117683683,59217191289,151687926023
%N A026599 a(n) = Sum_{j=0..2*i, i=0..n} A026584(i,j).
%H A026599 G. C. Greubel, <a href="/A026599/b026599.txt">Table of n, a(n) for n = 0..1000</a>
%H A026599 Amir Sapir, <a href="https://doi.org/10.1093/comjnl/47.1.20">The Tower of Hanoi with Forbidden Moves</a>, The Computer J. 47 (1) (2004) 20, case cyclic++, sequence c(n) (offset 1).
%H A026599 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-4).
%F A026599 G.f.: (1+x)/((1-x)*(1-x-4*x^2)). - _Ralf Stephan_, Feb 04 2004
%F A026599 From _Klaus Purath_, Feb 02 2021: (Start)
%F A026599 a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3).
%F A026599 a(n) = Sum_{j=0..n} A026597(j). (End)
%F A026599 a(n) = 2^n*(Fibonacci(n+2, 1/2) + Fibonacci(n+1, 1/2)) - 1/2. - _G. C. Greubel_, Dec 15 2021
%t A026599 LinearRecurrence[{2,3,-4}, {1,3,9}, 40] (* _G. C. Greubel_, Dec 15 2021 *)
%o A026599 (Magma) [n le 3 select 3^(n-1) else 2*Self(n-1) +3*Self(n-2) -4*Self(n-3): n in [1..41]]; // _G. C. Greubel_, Dec 15 2021
%o A026599 (Sage) [( (1+x)/((1-x)*(1-x-4*x^2)) ).series(x,n+1).list()[n] for n in (0..40)] # _G. C. Greubel_, Dec 15 2021
%Y A026599 Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597 (first differences), A026598, A027282, A027283, A027284, A027285, A027286.
%Y A026599 Cf. A006131, A026581.
%K A026599 nonn,easy
%O A026599 0,2
%A A026599 _Clark Kimberling_