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Search: id:A111314
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| A111314 |
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a(n) = a(n-1) + a(n-2) + 2 where a(0) = a(1) = 1. |
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+0
3
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| 1, 1, 4, 7, 13, 22, 37, 61, 100, 163, 265, 430, 697, 1129, 1828, 2959, 4789, 7750, 12541, 20293, 32836, 53131, 85969, 139102, 225073, 364177, 589252, 953431, 1542685, 2496118, 4038805, 6534925, 10573732, 17108659, 27682393, 44791054, 72473449
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
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FORMULA
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a(n)=2Fib(n+1)-Fib(n+2)+Fib(n+3)-2. - Robert G. Wilson v, Nov 10 2005
G.f.: (2x^2-x+1)/((x-1)(x^2+x-1)) - T. D. Noe, Oct 19 2007
a(n)=F(n)+F(n+4)-2, n>=-1 {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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with(combinat): seq(fibonacci(n)+fibonacci(n+4)-2, n=-1..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
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MATHEMATICA
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a[0] = a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + 2; Table[ a[n], {n, 0, 36}] (* Robert G. Wilson v *)
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PROGRAM
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sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(1, 1, 1, 1, lambda n: 2) sage: [it.next() for i in xrange(1, 38)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2008
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CROSSREFS
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Cf. A000045, A000071.
Sequence in context: A147487 A008471 A156622 this_sequence A139217 A038391 A090854
Adjacent sequences: A111311 A111312 A111313 this_sequence A111315 A111316 A111317
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KEYWORD
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easy,nonn
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AUTHOR
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Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 03 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 07 2005
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