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

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

Offset

1,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

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

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(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=3, a(3)=14. - Harvey P. Dale, Oct 01 2011

E.g.f.: exp(x)*(16 - 14*x + 9*x^2)/2. - Stefano Spezia, Dec 25 2022

Maple

seq((16-23*n+9*n^2)*1/2, n=1..40); # Emeric Deutsch, May 07 2008

Mathematica

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

Prog

(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

Crossrefs

Cf. A000217, A007318, A064226.

Sequence in context: A033991 A155154 A081269 * A064226 A077288 A094627

Adjacent sequences: A140061 A140062 A140063 * A140065 A140066 A140067

Keyword

nonn,easy

Author

Gary W. Adamson, May 03 2008

Extensions

More terms from R. J. Mathar and Emeric Deutsch, May 06 2008

Status

approved