A191869 First differences of the dying rabbits sequence A000044.

0, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 88, 143, 231, 373, 603, 974, 1574, 2543, 4109, 6639, 10727, 17332, 28004, 45248, 73109, 118126, 190862, 308385, 498273, 805084, 1300814, 2101789, 3395964, 5487026, 8865658, 14324680, 23145090, 37396661, 60423625

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 18 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000044.

Programs

Mathematica

A000044 = CoefficientList[Series[1/(1 - z - z^3 - z^5 - z^7 - z^9 - z^11), {z, 0, 200}], z]; GetDiff[seq_List] := Drop[seq, 1] - Drop[seq, -1]; A191869 = GetDiff[A000044]

PARI

A191869_list=Vec((-x^11-x^9-x^7-x^5-x^3)/(x^11+x^9+x^7+x^5+x^3+x-1)+O(x^99)) /* returns a list of the first 96 nonzero terms, a(3)...a(99) */

PARI

A191869(n)=polcoeff((1+x^2+x^4+x^6+x^8)/(1-x-x^3-x^5-x^7-x^9-x^11+O(x^max(1,n-2))),n-3)  \\ M. F. Hasler, Jun 19 2011

Formula

G.f.: x^3(1 + x + x^2 + x^3 + x^4)(1 - x + x^2 - x^3 + x^4)/(1 - x - x^3 - x^5 - x^7 - x^9 - x^11). - Charles R Greathouse IV, Jun 19 2011