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A140064 a(n) = (9*n^2 - 23*n + 16)/2. 5

%I

%S 1,3,14,34,63,101,148,204,269,343,426,518,619,729,848,976,1113,1259,

%T 1414,1578,1751,1933,2124,2324,2533,2751,2978,3214,3459,3713,3976,

%U 4248,4529,4819,5118,5426,5743,6069,6404,6748

%N a(n) = (9*n^2 - 23*n + 16)/2.

%C Binomial transform of [1, 2, 9, 0, 0, 0,...].

%H G. C. Greubel, <a href="/A140064/b140064.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F A007318 * [1, 2, 9, 0, 0, 0,...].

%F a(n) = A000217(n) + 8*A000217(n-2). - _R. J. Mathar_, May 06 2008

%F O.g.f.: x*(1+8*x^2)/(1-x)^3. - _R. J. Mathar_, May 06 2008

%F 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

%F a(n) = A064226(n-2), n>1. - _R. J. Mathar_, Jul 31 2008

%F a(n) = a(n-1) + 9*n - 16, a(1)=1. - _Vincenzo Librandi_, Nov 24 2010

%F 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

%p seq((16-23*n+9*n^2)*1/2,n=1..40); # _Emeric Deutsch_, May 07 2008

%t Table[(9n^2-23n+16)/2,{n,40}] (* or *) LinearRecurrence[{3,-3,1},{1,3,14},40] (* _Harvey P. Dale_, Oct 01 2011 *)

%o (MAGMA) [ n eq 1 select 1 else Self(n-1)+9*n-16: n in [1..50] ];

%o (PARI) x='x+O('x^50); Vec(x*(1+8*x^2)/(1-x)^3) \\ _G. C. Greubel_, Feb 18 2017

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, May 03 2008

%E More terms from _R. J. Mathar_ and _Emeric Deutsch_, May 06 2008

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Last modified May 17 18:44 EDT 2021. Contains 343987 sequences. (Running on oeis4.)