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A022403
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a(0)=a(1)=3; thereafter a(n) = a(n-1) + a(n-2) + 1.
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3
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3, 3, 7, 11, 19, 31, 51, 83, 135, 219, 355, 575, 931, 1507, 2439, 3947, 6387, 10335, 16723, 27059, 43783, 70843, 114627, 185471, 300099, 485571, 785671, 1271243, 2056915, 3328159, 5385075, 8713235, 14098311, 22811547, 36909859, 59721407, 96631267, 156352675, 252983943, 409336619, 662320563
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: ( 3-3*x+x^2 ) / ( (x-1)*(x^2+x-1) ). (End)
a(n) = (-1 + (2^(1-n)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n))) / sqrt(5)). - Colin Barker, Mar 02 2018
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MATHEMATICA
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RecurrenceTable[{a[0]==a[1]==3, a[n]==a[n-1]+a[n-2]+1}, a, {n, 40}] (* or *) LinearRecurrence[{2, 0, -1}, {3, 3, 7}, 50] (* Harvey P. Dale, Jan 10 2021 *)
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PROG
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(PARI) for(n=0, 40, print1(4*fibonacci(n+1) -1, ", ")) \\ G. C. Greubel, Mar 01 2018
(Magma) [4*Fibonacci(n+1) - 1: n in [0..40]]; // G. C. Greubel, Mar 01 2018
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CROSSREFS
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See A022406 for a similar sequence.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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