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A140065 a(n) = (7*n^2 - 17*n + 12)/2. 1
1, 3, 12, 28, 51, 81, 118, 162, 213, 271, 336, 408, 487, 573, 666, 766, 873, 987, 1108, 1236, 1371, 1513, 1662, 1818, 1981, 2151, 2328, 2512, 2703, 2901, 3106, 3318, 3537, 3763, 3996, 4236, 4483, 4737, 4998, 5266, 5541, 5823, 6112, 6408, 6711, 7021, 7338 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Binomial transform of [1, 2, 7, 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

A007318 * [1, 2, 7, 0, 0, 0,...].

a(n) = A000217(n) + 6*A000217(n-2) = (A140064(n) + A140066(n))/2. - R. J. Mathar, May 06 2008

o.g.f.: x*(1+6*x^2)/(1-x)^3. - Alexander R. Povolotsky, May 06 2008

a(n) = 7*n + a(n-1) - 12 for n>1, a(1)=1. - Vincenzo Librandi, Jul 08 2010

EXAMPLE

a(4) = 28 = (1, 3, 3, 1) * (1, 2, 7, 0) = (1 + 6 + 21 + 0).

MAPLE

seq((12-17*n+7*n^2)*1/2, n=1..40); # Emeric Deutsch, May 07 2008

MATHEMATICA

Table[(7 n^2 - 17 n + 12)/2, {n, 1, 50}] (* Bruno Berselli, Mar 12 2015 *)

LinearRecurrence[{3, -3, 1}, {1, 3, 12}, 50] (* Harvey P. Dale, May 28 2017 *)

PROG

(PARI) x = 'x + O('x^50); Vec(x*(1+6*x^2)/(1-x)^3) \\ G. C. Greubel, Feb 23 2017

CROSSREFS

Cf. A000217.

Sequence in context: A083539 A237426 A066643 * A294418 A115549 A005995

Adjacent sequences:  A140062 A140063 A140064 * A140066 A140067 A140068

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, May 03 2008

EXTENSIONS

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

More terms from Vladimir Joseph Stephan Orlovsky, Oct 25 2008

STATUS

approved

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Last modified October 22 21:09 EDT 2018. Contains 316505 sequences. (Running on oeis4.)