A127839 - OEIS

A127839

a(1)=1, a(2)=...=a(5)=0, a(n) = a(n-5) + a(n-4) for n > 5.

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 3, 3, 1, 1, 4, 6, 4, 2, 5, 10, 10, 6, 7, 15, 20, 16, 13, 22, 35, 36, 29, 35, 57, 71, 65, 64, 92, 128, 136, 129, 156, 220, 264, 265, 285, 376, 484, 529, 550, 661, 860, 1013, 1079, 1211

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

OFFSET

1,15

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Sadjia Abbad and Hacène Belbachir, The r-Fibonacci polynomial and its companion sequences linked with some classical sequences, Integers (2025), Vol. 25, Art. No. A38. See p. 17.

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

FORMULA

Binet-like formula: a(n) = Sum_{i=1...5} (r_i^n)/(4(r_i)^2+5(r_i)) where r_i is a root of x^5=x+1.

G.f.: x*(x^4-1)/(x^5+x^4-1). - Harvey P. Dale, Mar 19 2012

a(n) = A017827(n-6) for n >= 6. - R. J. Mathar, May 09 2013

MATHEMATICA

LinearRecurrence[{0, 0, 0, 1, 1}, {1, 0, 0, 0, 0}, 70] (* Harvey P. Dale, Mar 19 2012 *)

CROSSREFS

Sequence in context: A321752 A349839 A247919 * A017827 A279778 A094266

Adjacent sequences: A127836 A127837 A127838 * A127840 A127841 A127842

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved