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Search: id:A027961
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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; listen)
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OFFSET
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1,2
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LINKS
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E. S. Egge and T. Mansour, Restricted permutations, Fibonacci numbers, and k-generalized Fibonacci numbers.
Dan Sewell Ward, Modified Fibonacci Sequence.
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FORMULA
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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
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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
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CROSSREFS
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T(n,n+1), T given by A027960.
Sequence in context: A011896 A024624 A098196 this_sequence A018921 A103536 A011970
Adjacent sequences: A027958 A027959 A027960 this_sequence A027962 A027963 A027964
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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