

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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.


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 [Apparently unpublished as of May 2016]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


MAPLE

P:=proc(n) local a, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, i; a0:=1; a1:=0; a2:=0; a3:=0; a4:=0; a5:=0; a6:=0; a7:=0; a8:=0; print(a0); print(a1); print(a2); print(a3); print(a4); print(a5); print(a6); print(a7); print(a8); for i from 0 by 1 to n do a:=a0+a1; a0:=a1; a1:=a2; a2:=a3; a3:=a4; a4:=a5; a5:=a6; a6:=a7: a7:=a8; a8:=a; print(a); od; end: P(100); # Paolo P. Lava, Jun 28 2007


PROG

(PARI) Vec(x*(1x)*(1+x)*(1+x^2)*(1+x^4)/(1x^8x^9) + O(x^100)) \\ Colin Barker, May 30 2016


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



