A013915 a(n) = F(n) + L(n) + n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively.

3, 3, 7, 10, 16, 24, 37, 57, 89, 140, 222, 354, 567, 911, 1467, 2366, 3820, 6172, 9977, 16133, 26093, 42208, 68282, 110470, 178731, 289179, 467887, 757042, 1224904, 1981920, 3206797, 5188689, 8395457, 13584116, 21979542, 35563626, 57543135

Offset: 0

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3, -2, -1, 1).

Programs

Magma

I:=[3, 3, 7, 10]; [n le 4 select I[n] else 3*Self(n-1)-2*Self(n-2)-Self(n-3)+Self(n-4): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012

Mathematica

LinearRecurrence[{3,-2,-1, 1},{3,3,7,10},40] (* Vincenzo Librandi, Feb 14 2012 *)

Formula

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

From R. J. Mathar, Nov 04 2009: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4).

G.f.: (-3 + 6*x - 4*x^2 + 2*x^3)/((x^2+x-1) * (x-1)^2).

a(n) = n + A013655(n). (End)

Extensions

More terms from Erich Friedman