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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Gary W. Adamson, May 03 2008

Keywords

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).
		

Crossrefs

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