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
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.
Programs
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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 *) -
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
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Python
print([3*4**n//7 for n in range(1,24)]) # Karl V. Keller, Jr., Mar 18 2021
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) = floor(3*4^n/7). - Karl V. Keller, Jr., Mar 18 2021
Comments