A103378 a(n) = a(n-10) + a(n-11) for n > 11, and a(n) = 1 for 1 <= n <= 11.
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
Examples
a(52)=17 because a(52)=a(52-10)+a(52-11) = a(42)+a(41) = 9 + 8.
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1,1).
Programs
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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
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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 *) -
PARI
Vec((x^10-1)/(x-1)/(1-x^10-x^11)+O(x^80)) \\ M. F. Hasler, Sep 19 2015
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
Extensions
Corrected and extended by R. J. Mathar, Nov 22 2007
Edited by M. F. Hasler, Sep 19 2015