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A182228
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a(n) = 3*a(n-2) - a(n-1) for n > 1, a(0) = 0, a(1) = 1.
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6
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0, 1, -1, 4, -7, 19, -40, 97, -217, 508, -1159, 2683, -6160, 14209, -32689, 75316, -173383, 399331, -919480, 2117473, -4875913, 11228332, -25856071, 59541067, -137109280, 315732481, -727060321, 1674257764, -3855438727, 8878212019, -20444528200, 47079164257, -108412748857
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: x/(1 + x - 3*x^2). (End)
G.f.: 1 - Q(0), where Q(k) = 1 + 3*x^2 - (k+2)*x + x*(k+1 - 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 06 2013
E.g.f.: (-1/sqrt(13))*(exp(-(1+sqrt(13))*x/2) - exp(-(1-sqrt(13))*x/2)). - G. C. Greubel, Aug 30 2015
a(n) = (-(-1)^n/sqrt(13))*(((1 + sqrt(13))/2)^n - ((1 - sqrt(13))/2)^n). - Taras Goy, Jul 17 2018
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MATHEMATICA
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RecurrenceTable[{a[n]== - a[n-1] + 3*a[n-2], a[0]== 0, a[1]== 1}, a, {n, 0, 200}] (* G. C. Greubel, Aug 30 2015 *)
LinearRecurrence[{-1, 3}, {0, 1}, 40] (* Harvey P. Dale, Oct 23 2016 *)
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PROG
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(Python)
prpr = 0
prev = 1
for i in range(2, 55):
current = prpr*3-prev
print (current, end=', ')
prpr = prev
prev = current
(Magma) [n le 2 select n-1 else -Self(n-1) + 3*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Aug 31 2015
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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