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A127193
A 9th-order Fibonacci sequence.
17
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...
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
KEYWORD
nonn,easy
AUTHOR
Luis A Restrepo (luisiii(AT)mac.com), Jan 07 2007
STATUS
approved