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A013915
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a(n) = F(n)+L(n)+n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively.
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1
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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; internal format)
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OFFSET
| 0,1
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = a(n-1)+a(n-2)-n+3.
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). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 04 2009]
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MATHEMATICA
| LinearRecurrence[{3, -2, -1, 1}, {3, 3, 7, 10}, 40] (* Vincenzo Librandi, Feb 14 2012 *)
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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
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CROSSREFS
| Sequence in context: A161618 A202873 A157933 * A136445 A052989 A022403
Adjacent sequences: A013912 A013913 A013914 * A013916 A013917 A013918
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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