A045928 The generalized Connell sequence C_{3,2}.

1, 2, 5, 8, 9, 12, 15, 18, 21, 22, 25, 28, 31, 34, 37, 40, 41, 44, 47, 50, 53, 56, 59, 62, 65, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 177

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Examples

			From _Michel Marcus_, Apr 02 2013: (Start)
As a triangle, sequence begins:
  1;
  2,  5,  8;
  9, 12, 15, 18, 21;
  ...
(End)
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, J. Integer Sequences, Vol. 2, 1999, #99.1.7.

Programs

Haskell

a045928 n = 3 * n - 2 * floor (1 + sqrt (fromIntegral n - 1))
-- Reinhard Zumkeller, Aug 09 2015

Mathematica

Table[3*n-2*Floor[1+Sqrt[n-1]],{n,70}] (* Harvey P. Dale, Apr 19 2019 *)

PARI

lista(nrow, m=3, r=2) = {a = 1; for (irow = 1, nrow, for (k = 1, 1 + r*(irow -1), print1(a, ", "); a += m;); a += 1 - m;);} \\ Michel Marcus, Apr 02 2013

Formula

C(n, m, r) = n*m - (m - 1)*floor((3*r - 2 + sqrt(8*r*(n - 1) + (r - 2)^2)) / (2*r)) with m=3 and r=2, thus a(n) = 3*n - 2*floor(1 + sqrt(n-1)). - Michel Marcus, Apr 02 2013

Extensions

More terms from jeroen.lahousse(AT)icl.com

Typo in formula fixed by Reinhard Zumkeller, Aug 09 2015