A130766 3n+2 sandwiched by tripled 3n+1 .

1, 1, 1, 2, 4, 4, 4, 5, 7, 7, 7, 8, 10, 10, 10, 11, 13, 13, 13, 14, 16, 16, 16, 17, 19, 19, 19, 20, 22, 22, 22, 23, 25, 25, 25, 26, 28, 28, 28, 29, 31, 31, 31, 32, 34, 34, 34, 35, 37, 37, 37, 38, 40, 40, 40, 41, 43, 43, 43, 44, 46, 46, 46, 47, 49, 49, 49, 50, 52, 52, 52, 53, 55

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

From Chai Wah Wu, Jun 17 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 4.

G.f.: (x^4 + x^3 + 1)/(x^5 - x^4 - x + 1). (End)

a(n) = 2*floor(n/4) + floor((n+1)/4) + 1. - Ridouane Oudra, Jan 26 2024

Sum_{n>=0} (-1)^n/a(n) = Pi/(3*sqrt(3)) (A073010). - Amiram Eldar, Feb 11 2024

Mathematica

CoefficientList[Series[(x^4 + x^3 + 1) / (x^5 - x^4 - x + 1), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 18 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 1, 1, 2, 4}, 100] (* Harvey P. Dale, Apr 18 2023 *)

Prog

(Magma) I:=[1, 1, 1, 2, 4]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..80]]; // Vincenzo Librandi, Jun 18 2016

Crossrefs

Cf. A073010.

Sequence in context: A132345 A178976 A352426 * A227190 A284581 A284560

Adjacent sequences: A130763 A130764 A130765 * A130767 A130768 A130769

Keyword

nonn

Author

Paul Curtz, Aug 18 2007

Status

approved