A103379 a(n) = a(n-11) + a(n-12).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 12, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 21, 27, 31, 32, 32, 32, 32, 32, 32, 32, 33, 38, 48, 58, 63, 64, 64, 64, 64, 64, 64, 65, 71, 86, 106, 121, 127

Offset: 1

Author

Jonathan Vos Post, Feb 15 2005

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,1,1).

Crossrefs

Cf. A079398, A103372-A103378, A103380, A103389, A103399.

Programs

Maple

A103379 := proc(n) option remember ; if n <= 12 then 1; else procname(n-11)+procname(n-12) ; fi; end: for n from 1 to 120 do printf("%d,",A103379(n)) ; od: # R. J. Mathar, Aug 30 2008

Mathematica

SemiprimeQ[n_]:=Plus@@FactorInteger[n][[All, 2]]?2; k11; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103379=Array[a, 100] A103389=Union[Select[Array[a, 1000], PrimeQ]] A103399=Union[Select[Array[a, 300], SemiprimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Ray Chandler and Robert G. Wilson v *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,1,1},{1,1,1,1,1,1,1,1,1,1,1,1},100] (* Harvey P. Dale, Jan 31 2015 *)

Formula

For n>12: a(n) = a(n-11) + a(n-12). a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = a(10) = a(11) = a(12) = 1.

G.f.: x*(1-x^11) / ((1-x)*(1-x^11-x^12)). - Colin Barker, Mar 26 2013

Extensions

Corrected from a(11) on by R. J. Mathar, Aug 30 2008