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A144459
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a(n) = (3*n+1)*(5*n+1).
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1
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1, 24, 77, 160, 273, 416, 589, 792, 1025, 1288, 1581, 1904, 2257, 2640, 3053, 3496, 3969, 4472, 5005, 5568, 6161, 6784, 7437, 8120, 8833, 9576, 10349, 11152, 11985, 12848, 13741, 14664, 15617, 16600, 17613, 18656, 19729, 20832, 21965, 23128, 24321, 25544, 26797, 28080
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OFFSET
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0,2
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COMMENTS
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This appears in a "diagonal" scan through the numerators of the fractions of the hydrogen spectrum: A005563(4), A061037(9), A061039(13), etc.
a(n) mod 9 is a sequence of period length 9: repeat 1, 6, 5, 7, 3, 2, 4, 0, 8 (a permutation of A142069).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = A016777(n)*A016861(n).
a(n) mod 10 = A131579(n+7).
G.f.: (1+21*x+8*x^2) / (1-x)^3 . - R. J. Mathar, Jul 01 2011
a(0)=1, a(1)=24, a(2)=77, a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Harvey P. Dale, May 02 2015
E.g.f.: (1 + 23*x + 15*x^2)*exp(x). - G. C. Greubel, Sep 20 2018
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MATHEMATICA
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Table[(3n+1)(5n+1), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 24 , 77}, 50] (* Harvey P. Dale, Jul 16 2014 *)
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PROG
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(MAGMA) [(3*n+1)*(5*n+1): n in [0..40]]; // Vincenzo Librandi, Aug 07 2011
(PARI) a(n)=(3*n+1)*(5*n+1) \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Sequence in context: A211596 A214397 A048352 * A290710 A206010 A124140
Adjacent sequences: A144456 A144457 A144458 * A144460 A144461 A144462
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Oct 08 2008
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STATUS
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approved
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