A037793 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 3,2,1,0.

3, 14, 57, 228, 915, 3662, 14649, 58596, 234387, 937550, 3750201, 15000804, 60003219, 240012878, 960051513, 3840206052, 15360824211, 61443296846, 245773187385, 983092749540, 3932370998163, 15729483992654, 62917935970617, 251671743882468, 1006686975529875, 4026747902119502

Offset

1,1

Links

Table of n, a(n) for n=1..26.

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

Formula

a(n) = 4*a(n-1) + a(n-4) - 4*a(n-5); a(1)=3, a(2)=14, a(3)=57, a(4)=228, a(5)=915. - Harvey P. Dale, Jun 01 2014

G.f.: x*(3 + 2*x + x^2)/((x - 1)*(4*x - 1)*(1 + x)*(x^2 + 1)). - R. J. Mathar, May 01 2015

E.g.f.: (76*cosh(4*x) - 51*cosh(x) - 25*cos(x) + 76*sinh(4*x) - 34*sinh(x) - 15*sin(x))/85. - Stefano Spezia, May 28 2023

Mathematica

Module[{nn=30, per}, per=PadRight[{}, nn, {3, 2, 1, 0}]; Table[ FromDigits[ Take[ per, n], 4], {n, nn}]] (* or *) LinearRecurrence[{4, 0, 0, 1, -4}, {3, 14, 57, 228, 915}, 30] (* Harvey P. Dale, Jun 01 2014 *)

Prog

(PARI) a(n) = 76<<(2*n) \ 85; \\ Kevin Ryde, May 28 2023

Crossrefs

Sequence in context: A111468 A052412 A353095 * A037093 A135926 A015523

Adjacent sequences: A037790 A037791 A037792 * A037794 A037795 A037796

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

a(24)-a(26) from Stefano Spezia, May 28 2023

Status

approved