A097280 Perimeter of integer triangle (A001611(n), A001611(n+1), A001611(n+2)).

5, 7, 9, 13, 19, 29, 45, 71, 113, 181, 291, 469, 757, 1223, 1977, 3197, 5171, 8365, 13533, 21895, 35425, 57317, 92739, 150053, 242789, 392839, 635625, 1028461, 1664083, 2692541, 4356621, 7049159, 11405777, 18454933, 29860707, 48315637

Offset

0,1

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Formula

a(n) = 2*A001611(n+2) + 1;

a(n) = a(n-1) + 2*A000045(n).

a(n) = A001611(n) + A001611(n+1) + A001611(n+2).

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

G.f.: -(5*x^2 + 3*x - 5) / ((x-1)*(x^2 + x - 1)). - Colin Barker, Apr 10 2013

a(n) = 2*Fibonacci(n+2) + 3. - Greg Dresden, Oct 10 2020

Mathematica

Fibonacci[Range[2, 5! ]]*2+3 (* Vladimir Joseph Stephan Orlovsky, Mar 19 2010 *)
LinearRecurrence[{2, 0, -1}, {5, 7, 9}, 40] (* Harvey P. Dale, Nov 12 2015 *)

Crossrefs

Cf. A000045, A001611, A097281.

Sequence in context: A231271 A359198 A039504 * A155732 A218851 A211184

Adjacent sequences: A097277 A097278 A097279 * A097281 A097282 A097283

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 04 2004

Extensions

Corrected by T. D. Noe, Oct 25 2006

Status

approved