A037604 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,2,3.

1, 6, 27, 109, 438, 1755, 7021, 28086, 112347, 449389, 1797558, 7190235, 28760941, 115043766, 460175067, 1840700269, 7362801078, 29451204315, 117804817261, 471219269046, 1884877076187, 7539508304749, 30158033218998

Offset

1,2

Comments

Convolution of A000302 with A010882. - Philippe Deléham, Mar 24 2013

Links

Michael De Vlieger, Table of n, a(n) for n = 1..1661

Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4).

Index entries for 2-automatic sequences.

Formula

G.f.: x*(1+2x+3*x^2)/((1-x)*(1-4x)*(1+x+x^2)). - Philippe Deléham, Mar 24 2013

a(n) = 4*a(n-1) + a(n-3) -4*a(n-4) for n > 5, a(1) = 1, a(2) = 6, a(3) = 27, a(4) = 109, a(5) = 438. - Philippe Deléham, Mar 24 2013

a(n+2) = 6*A033140(n) + A191597(n+2). - Philippe Deléham, Mar 24 2013

A007090(a(n)) = A037610(n). - R. J. Mathar, Apr 27 2015

a(n) = floor(3*4^n/7). - Karl V. Keller, Jr., Mar 18 2021

Mathematica

Rest@ CoefficientList[Series[x (1 + 2 x + 3 x^2)/((1 - x) (1 - 4 x) (1 + x + x^2)), {x, 0, 23}], x] (* Michael De Vlieger, Mar 19 2021 *)
Table[FromDigits[PadRight[{}, n, {1, 2, 3}], 4], {n, 30}] (* or *) LinearRecurrence[{4, 0, 1, -4}, {1, 6, 27, 109}, 30] (* Harvey P. Dale, May 07 2023 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 1, 0, 4]^(n-1)*[1; 6; 27; 109])[1, 1] \\ Charles R Greathouse IV, Feb 13 2017
(Python) print([3*4**n//7 for n in range(1, 24)]) # Karl V. Keller, Jr., Mar 18 2021

Crossrefs

Cf. A000302, A010882.

Sequence in context: A318638 A094829 A055145 * A022634 A094788 A221863

Adjacent sequences: A037601 A037602 A037603 * A037605 A037606 A037607

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved