A060823 4-wave sequence beginning with 2's with middles dropped.

2, 2, 8, 20, 60, 170, 492, 1414, 4074, 11728, 33772, 97240, 279994, 806208, 2321386, 6684162, 19246280, 55417452, 159568196, 459458306, 1322957468, 3809304206, 10968454314, 31582405472, 90937912212, 261845282320, 753953441490

Offset: 2

Author

Jason Earls, May 01 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 2..200
• F. v. Lamoen, Wave sequences
• Index entries for linear recurrences with constant coefficients, signature (2,3,-1,-1).

Crossrefs

Cf. A038197.

Programs

Mathematica

LinearRecurrence[{2,3,-1,-1},{2,2,8,20},30] (* Harvey P. Dale, Aug 31 2016 *)

PARI

{ for (n=2, 200, if (n>5, a=2*a1 + 3*a2 - a3 - a4; a4=a3; a3=a2; a2=a1; a1=a, if (n==2, a=a4=2, if (n==3, a=a3=2, if (n==4, a=a2=8, a=a1=20)))); write("b060823.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 12 2009

Formula

a(n) = 2*a(n-1) + 3*a(n-2) - a(n-3) - a(n-4). - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 22 2003

From R. J. Mathar, Jul 15 2009: (Start)

G.f.: -2*x^2*(-1+x+x^2)/((1+x)*(x^3-3*x+1)).

a(n) = 2*A006357(n-3). (End)