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

0,1

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A202873 A157933 A350394 * A136445 A326269 A052989

Adjacent sequences: A013912 A013913 A013914 * A013916 A013917 A013918

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman

Status

approved