|
%I #12 Apr 07 2020 21:00:11
%S 2,4,7,12,19,31,49,80,129,210,339,549,887,1436,2323,3760,6083,9843,
%T 15925,25768,41693,67462,109155,176617,285771,462388,748159,1210548,
%U 1958707,3169255,5127961,8297216,13425177,21722394,35147571,56869965,92017535,148887500
%N a(n) = a(n-1) + a(n-2) - a(n-3) +a(n-4) + a(n-5) for n >= 6, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 19, a(5) = 31.
%C Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->1000, 10->001, starting with 00; see A287372.
%H Clark Kimberling, <a href="/A287525/b287525.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 1, 1).
%F a(n) = a(n-1) + a(n-2) - a(n-3) +a(n-4) + a(n-5) for n >= 6, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 19, a(5) = 31.
%F G.f.: (-2 - 2*x - x^2 - 3*x^3 - 2*x^4 - x^5)/(-1 + x + x^2 - x^3 + x^4 + x^5).
%t Join[{2}, LinearRecurrence[{1, 1, -1, 1, 1}, {4, 7, 12, 19, 31}, 40]]
%Y Cf. A287372.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Jun 18 2017
|
