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

0,2

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).

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

Mathematica

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

Prog

(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
(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

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.

Sequence in context: A180488 A318860 A318818 * A061647 A207008 A077996

Adjacent sequences: A026596 A026597 A026598 * A026600 A026601 A026602

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved