

A127843


a(1) = 1, a(2) = ... = a(9) = 0, a(n) = a(n9)+a(n8) for n>9.


1



1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 2, 9
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OFFSET

1,27


COMMENTS

Part of the phi_k family of sequences defined by a(1)=1, a(2)=...=a(k)=0, a(n)=a(nk)+a(nk+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 A017867.  Georg Fischer, Oct 07 2018


REFERENCES

S. Suter, Binetlike 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 [Apparently unpublished as of May 2016]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 (0,0,0,0,0,0,0,1,1).


FORMULA

Binetlike formula: a(n) = Sum_{i=1..9} (r_i^n)/(8(r_i)^2+9(r_i)) where r_i is a root of x^9=x+1.
G.f.: x*(1x)*(1+x)*(1+x^2)*(1+x^4) / (1x^8x^9).  Colin Barker, May 30 2016


MATHEMATICA

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0}, 120] (* Harvey P. Dale, Jun 15 2017 *)
CoefficientList[Series[(1x)*(1+x)*(1+x^2)*(1+x^4) / (1x^8x^9), {x, 0, 50}], x] (* Stefano Spezia, Oct 08 2018 *)


PROG

(PARI) Vec(x*(1x)*(1+x)*(1+x^2)*(1+x^4)/(1x^8x^9) + O(x^100)) \\ Colin Barker, May 30 2016
(GAP) a:=[1, 0, 0, 0, 0, 0, 0, 0, 0];; for n in [10..90] do a[n]:=a[n8]+a[n9]; od; a; # Muniru A Asiru, Oct 07 2018


CROSSREFS

Sequence in context: A284095 A279593 A017867 * A154234 A091396 A173677
Adjacent sequences: A127840 A127841 A127842 * A127844 A127845 A127846


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



