A127193 A 9th-order Fibonacci sequence.

1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8185, 16353, 32673, 65281, 130433, 260609, 520705, 1040385, 2078721, 4153345, 8298505, 16580657, 33128641, 66192001, 132253569, 264246529, 527972353, 1054904321

Offset

1,10

Comments

9-Bonacci constant = 1.99802947...

Links

Robert Price, Table of n, a(n) for n = 1..1000

E. S. Croot, Notes on Linear Recurrence Sequences

M. A. Lerma, Recurrence Relations

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

Formula

For a(1)=...=a(9)=1, a(10)=9, a(n)= 2*a(n-1) - a(n-10). - Vincenzo Librandi, Dec 20 2010

G.f.: x*(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8+7*x^9)/(1-2*x+x^10). - G. C. Greubel, Jul 28 2017

Mathematica

LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1}, 40] (* Ray Chandler, Aug 01 2015 *)
With[{c=Table[1, {9}]}, LinearRecurrence[c, c, 40]] (* Harvey P. Dale, Apr 08 2016 *)

Prog

(PARI) x='x+O('x^50); Vec((x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9+7*x^10)/(1 -2*x+ x^10)) \\ G. C. Greubel, Jul 28 2017

Crossrefs

Cf. Fibonacci numbers A000045, tribonacci numbers A000213, tetranacci numbers A000288, pentanacci numbers A000322, hexanacci numbers A000383, 7th-order Fibonacci numbers A060455, octanacci numbers, A123526.

Sequence in context: A260477 A275543 A111733 * A262453 A197344 A146236

Adjacent sequences: A127190 A127191 A127192 * A127194 A127195 A127196

Keyword

nonn,easy

Author

Luis A Restrepo (luisiii(AT)mac.com), Jan 07 2007

Status

approved