A378499 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 0,3,2.

1, 4, 19, 78, 312, 1251, 5006, 20024, 80099, 320398, 1281592, 5126371, 20505486, 82021944, 328087779, 1312351118, 5249404472, 20997617891, 83990471566, 335961886264, 1343847545059, 5375390180238, 21501560720952, 86006242883811, 344024971535246

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((11/36)*4^n).

G.f.: z*(z^3+3*z^2+1)/((z-1)*(4*z-1)*(z^2+z+1)).

E.g.f.: (9 - 20*exp(x) + 11*exp(4*x) + 8*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2))/36. - Stefano Spezia, Nov 29 2024

Example

a(7) = 1032032_4 = 5006.
a(8) = 10320320_4 = 20024.

Mathematica

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

Crossrefs

Cf.: A378497, A037667, A037618, A037681, A378502. Periodic part of sequence rotated left relative to A378497.

Sequence in context: A130132 A037590 A359087 * A037681 A156760 A320088

Adjacent sequences: A378496 A378497 A378498 * A378500 A378501 A378502

Keyword

nonn,base,easy

Author

Jonathan Shadrach Gilbert, Nov 28 2024

Status

approved