|
%I #27 Jan 03 2024 17:31:59
%S 0,1,1,2,3,6,10,18,31,55,96,169,296,520,912,1601,2809,4930,8651,15182,
%T 26642,46754,82047,143983,252672,443409,778128,1365520,2396320,
%U 4205249,7379697,12950466,22726483,39882198,69988378,122821042,215535903,378239143,663763424
%N a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2; a(n) = a(n-1) + a(n-2) + a(n-4).
%C Essentially the same as A060945: a(0)=0 and a(n)=A060945(n-1) for n>=1.
%C lim(n->infinity) a(n+1)/a(n) = A109134 = 1.754877666..., the square of the absolute value of one of the complex-valued roots of the characteristic polynomial. [_R. J. Mathar_, Nov 01 2010]
%C The Ze4 sums, see A180662 for the definition of these sums, of the ‘Races with Ties’ triangle A035317 lead to this sequence. [_Johannes W. Meijer_, Jul 20 2011]
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1). [From _R. J. Mathar_, Oct 29 2010]
%F a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2; a(n) = a(n-1) + a(n-2) + a(n-4).
%F G.f.: x/(1-x-x^2-x^4). [_Franklin T. Adams-Watters_, Feb 25 2011]
%F a(n) = |A077930(n)| = ( |A056016(n+2)|-(-1)^n)/5. [_R. J. Mathar_, Oct 29 2010]
%F a(n) = A060945(n-1), n>1. [_R. J. Mathar_, Nov 03 2010]
%e a(7) = 18 = a(6) + a(5) + a(3) = 10 + 6 + 2.
%e a(7) = 18 = (1 0, 2, 0, 2, 0, 3) dot (10, 6, 3, 2, 1, 1, 1) = (10 + 3 + 2 + 3).
%t LinearRecurrence[{1,1,0,1},{0,1,1,2},40] (* _Harvey P. Dale_, Jun 20 2015 *)
%Y All of A060945, A077930, A181532 are variations of the same sequence. - _N. J. A. Sloane_, Mar 04 2012
%K easy,nonn
%O 0,4
%A _Gary W. Adamson_, Oct 28 2010
%E Values from a(9) on changed by _R. J. Mathar_, Oct 29 2010
%E Edited and a(0) added by _Franklin T. Adams-Watters_, Feb 25 2011
|
