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A140064
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a(n) = (9*n^2 - 23*n + 16)/2.
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5
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1, 3, 14, 34, 63, 101, 148, 204, 269, 343, 426, 518, 619, 729, 848, 976, 1113, 1259, 1414, 1578, 1751, 1933, 2124, 2324, 2533, 2751, 2978, 3214, 3459, 3713, 3976, 4248, 4529, 4819, 5118, 5426, 5743, 6069, 6404, 6748
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OFFSET
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1,2
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COMMENTS
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Binomial transform of [1, 2, 9, 0, 0, 0,...].
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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A007318 * [1, 2, 9, 0, 0, 0,...].
a(n) = A000217(n) + 8*A000217(n-2). - R. J. Mathar, May 06 2008
O.g.f.: x*(1+8*x^2)/(1-x)^3. - R. J. Mathar, May 06 2008
Ogf([1,3,14,34,63,101,148,204,269,343,426,518,619,729]) = (8*x^2 + 1)/(-x^3 + 3*x^2 - 3*x + 1) - Alexander R. Povolotsky, May 06 2008
a(n) = A064226(n-2), n>1. - R. J. Mathar, Jul 31 2008
a(n) = a(n-1) + 9*n - 16, a(1)=1. - Vincenzo Librandi, Nov 24 2010
a(1)=1, a(2)=3, a(3)=14, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Oct 01 2011
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MAPLE
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seq((16-23*n+9*n^2)*1/2, n=1..40); # Emeric Deutsch, May 07 2008
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MATHEMATICA
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Table[(9n^2-23n+16)/2, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 3, 14}, 40] (* Harvey P. Dale, Oct 01 2011 *)
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PROG
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(MAGMA) [ n eq 1 select 1 else Self(n-1)+9*n-16: n in [1..50] ];
(PARI) x='x+O('x^50); Vec(x*(1+8*x^2)/(1-x)^3) \\ G. C. Greubel, Feb 18 2017
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CROSSREFS
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Sequence in context: A033991 A155154 A081269 * A064226 A077288 A094627
Adjacent sequences: A140061 A140062 A140063 * A140065 A140066 A140067
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KEYWORD
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nonn,easy
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AUTHOR
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Gary W. Adamson, May 03 2008
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EXTENSIONS
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More terms from R. J. Mathar and Emeric Deutsch, May 06 2008
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STATUS
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approved
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