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

1, 3, 9, 23, 61, 155, 401, 1023, 2629, 6723, 17241, 44135, 113101, 289643, 742049, 1900623, 4868821, 12471315, 31946601, 81831863, 209618269, 536945723, 1375418801, 3523201695, 9024876901, 23117683683, 59217191289, 151687926023

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Amir Sapir, The Tower of Hanoi with Forbidden Moves, The Computer J. 47 (1) (2004) 20, case cyclic++, sequence c(n) (offset 1).
• Index entries for linear recurrences with constant coefficients, signature (2,3,-4).

Crossrefs

Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597 (first differences), A026598, A027282, A027283, A027284, A027285, A027286.

Cf. A006131, A026581.

Programs

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

Mathematica

LinearRecurrence[{2,3,-4}, {1,3,9}, 40] (* G. C. Greubel, Dec 15 2021 *)

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

Formula

G.f.: (1+x)/((1-x)*(1-x-4*x^2)). - Ralf Stephan, Feb 04 2004

From Klaus Purath, Feb 02 2021: (Start)

a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3).

a(n) = Sum_{j=0..n} A026597(j). (End)

a(n) = 2^n*(Fibonacci(n+2, 1/2) + Fibonacci(n+1, 1/2)) - 1/2. - G. C. Greubel, Dec 15 2021