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

1,2

Links

Table of n, a(n) for n=1..25.

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

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.

Example

a(7) = 1320320_4 = 7736.
a(8) = 13203203_4 = 30947.

Mathematica

Table[FromDigits[Join[{1}, PadRight[{}, n-1, {3, 2, 0}]], 4], {n, 30}].

Crossrefs

Cf. A378497, A378499, A037667, A037618.

Sequence in context: A055269 A026631 A037709 * A037611 A171472 A369201

Adjacent sequences: A378499 A378500 A378501 * A378503 A378504 A378505

Keyword

nonn,base,easy

Author

Jonathan Shadrach Gilbert, Dec 03 2024

Status

approved