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

0,4

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]

Links

Table of n, a(n) for n=0..38.

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

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]

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A172516 A102702 A077930 * A060945 A349904 A023359

Adjacent sequences: A181529 A181530 A181531 * A181533 A181534 A181535

Keyword

easy,nonn

Author

Gary W. Adamson, Oct 28 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

Status

approved