A378497 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 2,0,3.

1, 6, 24, 99, 398, 1592, 6371, 25486, 101944, 407779, 1631118, 6524472, 26097891, 104391566, 417566264, 1670265059, 6681060238, 26724240952, 106896963811, 427587855246, 1710351420984, 6841405683939, 27365622735758, 109462490943032, 437849963772131

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((7/18)*4^n).

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

E.g.f.: (9 - 10*exp(x) + 7*exp(4*x) - 2*exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)))/18. - Stefano Spezia, Nov 29 2024

Example

a(7) = 1203203_4 = 6371.
a(8) = 12032032_4 = 25486.

Mathematica

Table[FromDigits[Join[{1}, PadRight[{}, n-1, {2, 0, 3}]], 4], {n, 30}]
LinearRecurrence[{4, 0, 1, -4}, {1, 6, 24, 99}, 30] (* Harvey P. Dale, May 12 2026 *)

Crossrefs

Cf. A378499, A037667, A037618, A378502. Periodic part of sequence rotated right relative to A378499. Same first four terms as A037688, and similar formula.

Sequence in context: A048179 A117614 A037688 * A343116 A360036 A255471

Adjacent sequences: A378494 A378495 A378496 * A378498 A378499 A378500

Keyword

nonn,base,easy

Author

Jonathan Shadrach Gilbert, Nov 28 2024

Status

approved