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A037604
Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,2,3.
1
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
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
Sequence in context: A318638 A094829 A055145 * A022634 A094788 A221863
KEYWORD
nonn,base,easy
STATUS
approved