A023439 Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-9).

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 54, 87, 139, 223, 357, 572, 916, 1467, 2349, 3762, 6024, 9647, 15448, 24738, 39614, 63436, 101583, 162670, 260491, 417137, 667981, 1069670, 1712913, 2742969, 4392446, 7033832, 11263608, 18036949, 28883420, 46252388, 74066138, 118605613

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Links

• Floris P. van Doorn and Jasper Mulder, Table of n, a(n) for n = 0..2000
• 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,-1).

Crossrefs

See A000045 for the Fibonacci numbers.

Programs

Mathematica

LinearRecurrence[{1,1,0,0,0,0,0,0,-1},{0,1,1,2,3,5,8,13,21},40] (* Harvey P. Dale, Dec 19 2021 *)

Formula

G.f.: x / ( (x-1)*(1+x)*(x^7+x^5+x^3+x-1) ). - R. J. Mathar, Nov 29 2011