A037581 Base 9 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.

1, 12, 109, 984, 8857, 79716, 717445, 6457008, 58113073, 523017660, 4707158941, 42364430472, 381279874249, 3431518868244, 30883669814197, 277953028327776, 2501577254949985, 22514195294549868, 202627757650948813, 1823649818858539320, 16412848369726853881

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9,1,-9).

Formula

From Colin Barker, Dec 27 2012: (Start)

a(n) = (3^(1+2*n) + 2*(-1)^n - 5)/20.

a(n) = 9*a(n-1) + a(n-2) - 9*a(n-3).

G.f.: x*(3*x+1) / ((x-1)*(x+1)*(9*x-1)). (End)

E.g.f.: (3*(cosh(9*x) - cosh(x) + sinh(9*x)) - 7*sinh(x))/20. - Stefano Spezia, Oct 25 2023

Mathematica

CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (9 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
Module[{nn=30, d}, d=PadRight[{}, nn, {1, 3}]; Table[FromDigits[Take[d, n], 9], {n, nn}]] (* Harvey P. Dale, Jul 22 2015 *)

Prog

(Magma) [(3^(1+2*n)+2*(-1)^n-5)/20: n in [1..30]]; // Vincenzo Librandi, Oct 22 2013

Crossrefs

Sequence in context: A081200 A351161 A016214 * A177071 A081183 A069294

Adjacent sequences: A037578 A037579 A037580 * A037582 A037583 A037584

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Colin Barker, Dec 27 2012

Status

approved