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
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
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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)
Comments
Links
Crossrefs
Formula