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

Author

Jonathan Vos Post, Feb 15 2005

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A079398, A103372-A103377, A103379-A103380, A103388, A103398.

Programs

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 *)

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