A316937 a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n > 2, a(0)=3, a(1)=10, a(2)=26.
3, 10, 26, 62, 140, 306, 654, 1376, 2862, 5902, 12092, 24650, 50054, 101328, 204630, 412454, 830076, 1668514, 3350558, 6723008, 13481438, 27020190, 54133116, 108416282, 217075350, 434543536, 869722694, 1740473846, 3482611772, 6967916082, 13940188782, 27887426720
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).
Programs
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GAP
List([0..35],n->13*2^n-2*Fibonacci(n+5)); # Muniru A Asiru, Jul 22 2018
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Magma
I:=[3, 10, 26]; [n le 3 select I[n] else 3*Self(n-1)-Self(n-2)-2*Self(n-3): n in [1..40]];
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Magma
[((2^(-n)*(65*4^n + (1-Sqrt(5))^n*(-25 + 11*Sqrt(5)) - (1 + Sqrt(5))^n*(25 + 11*Sqrt(5)))) / 5): n in [0..20]]; // Vincenzo Librandi, Aug 24 2018
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Maple
seq(coeff(series((3+x-x^2)/((1-2*x)*(1-x-x^2)), x,n+1),x,n),n=0..35); # Muniru A Asiru, Jul 22 2018
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Mathematica
CoefficientList[Series[(3 + x - x^2) / ((1 - 2 x) (1 - x - x^2)), {x, 0, 33}], x] (* or *) RecurrenceTable[{a[n]==3 a[n-1] - a[n-2] - 2 a[n-3], a[0]==3, a[1]==10, a[2]==26}, a, {n, 0, 40}] f[n_] := 13*2^n - 2 Fibonacci[n + 5]; Array[f, 32, 0] (* or *) LinearRecurrence[{3, -1, -2}, {3, 10, 26}, 32] (* Robert G. Wilson v, Jul 21 2018 *) -
PARI
Vec((3 + x - x^2) / ((1 - 2*x)*(1 - x - x^2)) + O(x^40)) \\ Colin Barker, Jul 22 2018
Formula
G.f.: (3 + x - x^2) / ((1 - 2*x)*(1 - x - x^2)).
a(n) = 13*2^n - 2*Fibonacci(n+5) for n>0.
a(n) = (2^(-n)*(65*4^n + (1-sqrt(5))^n*(-25+11*sqrt(5)) - (1+sqrt(5))^n*(25+11*sqrt(5)))) / 5. - Colin Barker, Jul 22 2018
Comments