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A000044 Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n >= 13, a(n) = a(n-1)+a(n-2)-a(n-13).
(Formerly M0691 N0255)
5
1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 232, 375, 606, 979, 1582, 2556, 4130, 6673, 10782, 17421, 28148, 45480, 73484, 118732, 191841, 309967, 500829, 809214, 1307487, 2112571, 3413385, 5515174, 8911138, 14398164, 23263822, 37588502, 60733592, 98130253, 158553878, 256183302, 413927966, 668803781, 1080619176, 1746009572, 2821113574, 4558212008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A107358 is a more satisfactory version, but I have left the present sequence unchanged (except for making the definition clearer) since it has been in the OEIS so long.

Number of compositions of n into parts 1, 3, 5, 7, 9, and 11. - Joerg Arndt, Sep 05 2014

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

J. H. E. Cohn, Letter to the editor, Fib. Quart. 2 (1964), 108.

V. E. Hoggatt, Jr. and D. A. Lind, The dying rabbit problem, Fib. Quart. 7 (1969), 482-487.

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

FORMULA

G.f.: 1/(1 - z - z^3 - z^5 - z^7 - z^9 -z^11).

G.f. A(x) = 1 / (1 - x / (1 - x^2 / (1 + x^10 / (1 + x^2 / (1 - x^2 / (1 + x^6 / (1 + x^2 / (1 - x^2 / (1 + x^2))))))))). - Michael Somos, Jan 04 2013

For n >= 11, a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-7) + a(n-9) + a(n-11). - Eric M. Schmidt, Sep 04 2014

EXAMPLE

G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 13*x^7 + 21*x^8 + 34*x^9 + ...

MAPLE

with(combinat); f:=proc(n) option remember; if n=0 then RETURN(1); fi; if n <= 12 then RETURN(fibonacci(n)); fi; f(n-1)+f(n-2)-f(n-13); end;

MATHEMATICA

CoefficientList[Series[1/(1 - z - z^3 - z^5 - z^7 - z^9 - z^11), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011. *)

LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144}, 100] (* Harvey P. Dale, Mar 24 2012 *)

PROG

(MAGMA) [ n eq 1 select 1 else n le 13 select Fibonacci(n-1) else Self(n-1)+Self(n-2)-Self(n-13): n in [1..50] ]; // Klaus Brockhaus, Dec 21 2010

(PARI) Vec(1/(1-z-z^3-z^5-z^7-z^9-z^11)+O(z^50)) \\ Charles R Greathouse IV, Jun 10 2011

CROSSREFS

Cf. A107358. See A000045 for the Fibonacci numbers.

Sequence in context: A268133 A217737 A023442 * A107358 A243063 A248740

Adjacent sequences:  A000041 A000042 A000043 * A000045 A000046 A000047

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane; entry revised May 25 2005

EXTENSIONS

G.f. corrected by Charles R Greathouse IV, Jun 10 2011

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.