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A013915 a(n) = F(n) + L(n) + n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A161618 A202873 A157933 * 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

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)