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

Author

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

Keywords

• nonn
• easy

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).

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.

Programs

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 *)

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

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