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A103378
a(n) = a(n-10) + a(n-11) for n > 11, and a(n) = 1 for 1 <= n <= 11.
8
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 12, 15, 16, 16, 16, 16, 16, 16, 16, 17, 21, 27, 31, 32, 32, 32, 32, 32, 32, 33, 38, 48, 58, 63, 64, 64, 64, 64, 64, 65, 71, 86, 106, 121, 127, 128
OFFSET
1,12
FORMULA
G.f.: x*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9)/(1-x^10-x^11). - R. J. Mathar, Nov 22 2007
EXAMPLE
a(52)=17 because a(52)=a(52-10)+a(52-11) = a(42)+a(41) = 9 + 8.
MAPLE
A103378 := proc(n) option remember; if n <= 11 then 1 ; else A103378(n-10)+A103378(n-11) ; fi ; end: seq(A103378(n), n=1..78) ; # R. J. Mathar, Nov 22 2007
MATHEMATICA
k=10; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103377=Array[a, 100] N[Solve[x^10 - x - 1 == 0, x], 111][[2]]
LinearRecurrence[Join[Table[0, {9}], {1, 1}], Table[1, {11}], 80] (* Harvey P. Dale, Aug 14 2013 *)
PROG
(PARI) Vec((x^10-1)/(x-1)/(1-x^10-x^11)+O(x^80)) \\ M. F. Hasler, Sep 19 2015
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 15 2005
EXTENSIONS
Corrected and extended by R. J. Mathar, Nov 22 2007
Edited by M. F. Hasler, Sep 19 2015
STATUS
approved