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A027961
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Lucas(n+2) - 3.
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7
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1, 4, 8, 15, 26, 44, 73, 120, 196, 319, 518, 840, 1361, 2204, 3568, 5775, 9346, 15124, 24473, 39600, 64076, 103679, 167758, 271440, 439201, 710644, 1149848, 1860495, 3010346, 4870844, 7881193, 12752040, 20633236, 33385279, 54018518
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| E. S. Egge and T. Mansour, Restricted permutations, Fibonacci numbers and k-generalized Fibonacci numbers.
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FORMULA
| a(0)=0, a(1)=1, a(n)=a(n-1)+a(n-2)+3.
a(n) = A000204(n+2)-3 = A000045(2n+4)/A000045(n+2) - 3. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 05 2003
G.f.: x(1+2x)/[(1-x)*(1-x-x^2)]. Differences of A023537. - Ralf Stephan, Feb 07 2004
a(n) = A101220(3, 1, n) - Ross La Haye (rlahaye(AT)new.rr.com), Jan 28 2005
Sum of the first n Lucas numbers, that is, A000204(1) to A000204(n). - T. D. Noe (noe(AT)sspectra.com), Oct 10 2005
a(n)=F(n)+F(n+2)-3 n>=2 {where F(n) is the n-th Fibonacci number} - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+a[n-2]+3 od: seq(a[n], n=1..50); (Miklos Kristof (kristmikl(AT)freemail.hu), Mar 09 2005)
with(combinat): seq(fibonacci(n)+fibonacci(n+2)-3, n=2..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
g:=(1+z^2)/(1-z-z^2): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-3, n=3..37); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]
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MATHEMATICA
| a=0; b=1; lst={a, b}; Do[z=a+b+3; AppendTo[lst, z]; a=b; b=z, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 16 2010]
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PROG
| (MAGMA) [Lucas(n+2) - 3: n in [1..100]]; // Vincenzo Librandi, Apr 16 2011
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CROSSREFS
| T(n, n+1), T given by A027960.
Sequence in context: A011896 A024624 A098196 * A018921 A103536 A011970
Adjacent sequences: A027958 A027959 A027960 * A027962 A027963 A027964
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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