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A140064
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(9n^2 - 23n + 16)/2.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Binomial transform of [1, 2, 9, 0, 0, 0,...].
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| A007318 * [1, 2, 9, 0, 0, 0,...].
a(n)=A000217(n)+8*A000217(n-2). O.g.f.: x*(1+8x^2)/(1-x)^3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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 (pevnev(AT)juno.com), May 06 2008
a(n)=A064226(n-2), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2008]
a(n) = a(n-1)+9*n-16 (with a(1)=1). [From 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) [From Harvey P. Dale, Oct 01 2011]
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MAPLE
| seq((16-23*n+9*n^2)*1/2, n=1..40); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 07 2008
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MATHEMATICA
| Table[(9n^2-23n+16)/2, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 3, 14}, 40] (* From Harvey P. Dale, Oct 01 2011 *)
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PROG
| (MAGMA) [ n eq 1 select 1 else Self(n-1)+9*n-16: n in [1..50] ];
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CROSSREFS
| Sequence in context: A033991 A155154 A081269 * A064226 A077288 A094627
Adjacent sequences: A140061 A140062 A140063 * A140065 A140066 A140067
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 03 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), May 06 2008
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