A127844 a(1) = 1, a(2) = ... = a(10) = 0, a(n) = a(n-10)+a(n-9) for n>10.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 1, 7, 21, 35, 35, 21, 7, 1, 0, 1, 8, 28

Offset

1,30

Comments

Part of the phi_k family of sequences defined by a(1)=1,a(2)=...=a(k)=0, a(n)=a(n-k)+a(n-k+1) for n>k. phi_2 is a shift of the Fibonacci sequence and phi_3 is a shift of the Padovan sequence.

Apart from offset same as A017877. - Georg Fischer, Oct 07 2018

References

S. Suter, Binet-like formulas for recurrent sequences with characteristic equation x^k=x+1, preprint, 2007. [Apparently unpublished as of May 2016]

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

Binet-like formula: a(n) = Sum_{i=1..10} (r_i^n)/(9(r_i)^2+10(r_i)) where r_i is a root of x^10=x+1.

G.f.: x*(1-x)*(1+x+x^2)*(1+x^3+x^6) / (1-x^9-x^10). - Colin Barker, May 30 2016

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 100] (* Harvey P. Dale, Jun 18 2017 *)

Prog

(PARI) Vec(x*(1-x)*(1+x+x^2)*(1+x^3+x^6)/(1-x^9-x^10) + O(x^100)) \\ Colin Barker, May 30 2016
(GAP) a:=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0];;  for n in [11..90] do a[n]:=a[n-9]+a[n-10]; od; a; # Muniru A Asiru, Oct 07 2018

Crossrefs

Sequence in context: A124749 A350890 A331416 * A017877 A295976 A095683

Adjacent sequences: A127841 A127842 A127843 * A127845 A127846 A127847

Keyword

nonn,easy

Author

Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007

Status

approved