A181532 a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2; a(n) = a(n-1) + a(n-2) + a(n-4).

0, 1, 1, 2, 3, 6, 10, 18, 31, 55, 96, 169, 296, 520, 912, 1601, 2809, 4930, 8651, 15182, 26642, 46754, 82047, 143983, 252672, 443409, 778128, 1365520, 2396320, 4205249, 7379697, 12950466, 22726483, 39882198, 69988378, 122821042, 215535903, 378239143, 663763424

Offset: 0

Author

Gary W. Adamson, Oct 28 2010

Keywords

• easy
• nonn

Comments

Essentially the same as A060945: a(0)=0 and a(n)=A060945(n-1) for n>=1.

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]

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]

Examples

			a(7) = 18 = a(6) + a(5) + a(3) = 10 + 6 + 2.
a(7) = 18 = (1 0, 2, 0, 2, 0, 3) dot (10, 6, 3, 2, 1, 1, 1) = (10 + 3 + 2 + 3).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,0,1). [From _R. J. Mathar_, Oct 29 2010]

Crossrefs

All of A060945, A077930, A181532 are variations of the same sequence. - N. J. A. Sloane, Mar 04 2012

Programs

Mathematica

LinearRecurrence[{1,1,0,1},{0,1,1,2},40] (* Harvey P. Dale, Jun 20 2015 *)

Formula

a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2; a(n) = a(n-1) + a(n-2) + a(n-4).

G.f.: x/(1-x-x^2-x^4). [Franklin T. Adams-Watters, Feb 25 2011]

a(n) = |A077930(n)| = ( |A056016(n+2)|-(-1)^n)/5. [R. J. Mathar, Oct 29 2010]

a(n) = A060945(n-1), n>1. [R. J. Mathar, Nov 03 2010]

Extensions

Values from a(9) on changed by R. J. Mathar, Oct 29 2010

Edited and a(0) added by Franklin T. Adams-Watters, Feb 25 2011