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A127843 a(1) = 1, a(2) = ... = a(9) = 0, a(n) = a(n-9)+a(n-8) 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(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.

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 [Apparently unpublished as of May 2016]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

FORMULA

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

CROSSREFS

Sequence in context: A103522 A101108 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

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Last modified December 2 23:29 EST 2016. Contains 278694 sequences.