A166863 a(1)= 1; a(2)= 5; thereafter a(n)= a(n-1) + a(n-2) + 5.

1, 5, 11, 21, 37, 63, 105, 173, 283, 461, 749, 1215, 1969, 3189, 5163, 8357, 13525, 21887, 35417, 57309, 92731, 150045, 242781, 392831, 635617, 1028453, 1664075, 2692533, 4356613, 7049151, 11405769, 18454925, 29860699, 48315629, 78176333, 126491967

Offset: 1

Author

Geoff Ahiakwo, Oct 22 2009

Keywords

• easy
• nonn

Examples

			a(3) = 5 + 1 + 5 = 11.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Crossrefs

Cf. A001595, A154691.

Programs

Haskell

a166863 n = a166863_list !! (n-1)
a166863_list = 1 : zipWith (+) a166863_list (drop 3 $ map (* 2) a000045_list)
-- Reinhard Zumkeller, Nov 17 2013

Mathematica

2 * Fibonacci[Range[4,4! ]] - 5 (* Vladimir Joseph Stephan Orlovsky, Mar 19 2010 *)
RecurrenceTable[{a[1]==1,a[2]==5,a[n]==a[n-1]+a[n-2]+5},a,{n,40}] (* or *) LinearRecurrence[{2,0,-1},{1,5,11},40] (* Harvey P. Dale, Jan 29 2021 *)

Formula

a(n) = A154691(n) - 2 = 2*A000045(n+3) - 5. - R. J. Mathar, Oct 26 2009

From R. J. Mathar, Oct 26 2009: (Start)

a(n) = 2*a(n-1) - a(n-3).

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

a(n+1) = a(n) + 2*A000045(n+2). - Reinhard Zumkeller, Nov 17 2013

Extensions

Missing value for a(29) inserted by Reinhard Zumkeller, Nov 17 2013