A378502 a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 3,2,0.
1, 7, 30, 120, 483, 1934, 7736, 30947, 123790, 495160, 1980643, 7922574, 31690296, 126761187, 507044750, 2028179000, 8112716003, 32450864014, 129803456056, 519213824227, 2076855296910, 8307421187640, 33229684750563, 132918739002254, 531674956009016
Offset: 1
Examples
a(7) = 1320320_4 = 7736. a(8) = 13203203_4 = 30947.
Links
- Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4).
Programs
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Mathematica
Table[FromDigits[Join[{1}, PadRight[{}, n-1, {3, 2, 0}]], 4], {n, 30}]
Formula
a(n) = floor((17/36)*4^n).
G.f.: -x*(x^3-2*x^2-3*x-1)/((x-1)*(4*x-1)*(x^2+x+1)).
a(n) = 4^(n-1) + A037667(n-1) for n > 1.