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A140066 a(n) = (5*n^2 - 11*n + 8)/2. 3
1, 3, 10, 22, 39, 61, 88, 120, 157, 199, 246, 298, 355, 417, 484, 556, 633, 715, 802, 894, 991, 1093, 1200, 1312, 1429, 1551, 1678, 1810, 1947, 2089, 2236, 2388, 2545, 2707, 2874, 3046, 3223, 3405, 3592, 3784 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Binomial transform of [1, 2, 5, 0, 0, 0, ...].

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.

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

FORMULA

A007318 * [1, 2, 5, 0, 0, 0, ...].

From R. J. Mathar, May 06 2008: (Start)

a(n) = A000217(n) + 4*A000217(n-2).

O.g.f.: x*(1+4*x^2)/(1-x)^3. (End)

a(n) = (8 - 11*n + 5*n^2)/2. - Emeric Deutsch, May 07 2008

Ogf([1,3,10,22,39,61,88,120,157,199,246,298,355,417]) = (4*x^2 + 1)/(-x^3 + 3*x^2 - 3*x + 1). - Alexander R. Povolotsky, May 06 2008

a(n) = a(n-1) + 5*n - 8 (with 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)=10. - Harvey P. Dale, Jan 28 2012

EXAMPLE

a(4) = 22 = (1, 3, 3, 1) dot (1, 2, 5, 0) = (1, + 6 + 15 + 0).

MAPLE

seq((8-11*n+5*n^2)*1/2, n=1..40); # Emeric Deutsch, May 07 2008

MATHEMATICA

Table[(5n^2-11n+8)/2, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 3, 10}, 40] (* Harvey P. Dale, Jan 28 2012 *)

PROG

(PARI) a(n)=(5*n^2-11*n+8)/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Sequence in context: A174459 A326124 A122795 * A006503 A248851 A023554

Adjacent sequences:  A140063 A140064 A140065 * A140067 A140068 A140069

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

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Last modified April 22 16:32 EDT 2021. Contains 343177 sequences. (Running on oeis4.)