A140066 a(n) = (5*n^2 - 11*n + 8)/2.

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, 3981, 4183, 4390, 4602, 4819, 5041, 5268, 5500, 5737

Offset: 1

Author

Gary W. Adamson, May 03 2008

Keywords

• nonn
• easy

Comments

Binomial transform of [1, 2, 5, 0, 0, 0, ...] = A020821.

Examples

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

Crossrefs

Cf. A000217, A007318, A020821.

Programs

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 *)

PARI

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

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

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

E.g.f.: exp(x)*(4 - 3*x + 5*x^2/2) - 4. - Elmo R. Oliveira, Oct 31 2024

Extensions

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