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A117917
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a(n) = 3*a(n-1) + a(n-2) + n.
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1
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1, 4, 15, 52, 175, 582, 1927, 6370, 21045, 69514, 229597, 758316, 2504557, 8272000, 27320571, 90233728, 298021771, 984299058, 3250918963, 10737055966, 35462086881, 117123316630, 386832036793, 1277619427032, 4219690317913
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OFFSET
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0,2
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COMMENTS
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a(n)/a(n-1) tends to 3.30277563... = exp(ArcSinh(3/2)) (A098316).
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LINKS
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FORMULA
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O.g.f.: (1 - x + x^2)/((1-x)^2*(1 - 3*x - x^2)). - R. J. Mathar, Mar 17 2008
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MATHEMATICA
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LinearRecurrence[{5, -6, 1, 1}, {1, 4, 15, 52}, 30] (* Harvey P. Dale, Mar 21 2018 *)
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PROG
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(Magma) I:=[1, 4, 15, 52]; [n le 4 select I[n] else 5*Self(n-1) -6*Self(n-2) +Self(n-3) +Self(n-4): n in [1..31]]; // G. C. Greubel, Oct 22 2021
(Sage) [(2*lucas_number1(n+2, 3, -1) + 8*lucas_number1(n+1, 3, -1) - 3*n -5)/9 for n in (0..30)] # G. C. Greubel, Oct 22 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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