A033292 A Connell-like sequence: take 1 number = 1 (mod Q), 2 numbers = 2 (mod Q), 3 numbers = 3 (mod Q), etc., where Q = 3.

1, 2, 5, 6, 9, 12, 13, 16, 19, 22, 23, 26, 29, 32, 35, 36, 39, 42, 45, 48, 51, 52, 55, 58, 61, 64, 67, 70, 71, 74, 77, 80, 83, 86, 89, 92, 93, 96, 99, 102, 105, 108, 111, 114, 117, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 177, 180

Offset: 1

Author

Gary E. Stevens

Keywords

• nonn
• easy
• nice
• tabl

Comments

Left border of the triangle (1, 2, 6, 13, 23, 36, ...) = A143689 = A000326(n) - 3n, where A000326 = the pentagonal numbers, right border. - Gary W. Adamson, Aug 29 2008

Row sums = A143690: (1, 7, 27, 70, 145, 261, 427, 652, ...). - Gary W. Adamson, Aug 29 2008

Central terms = A136392. - Reinhard Zumkeller, Jan 18 2012

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
• Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, J. Integer Sequences, Vol. 2, 1999, #99.1.7.
• Gary E. Stevens, A Connell-Like Sequence, J. Integer Sequences, 1 (1998), #98.1.4.

Programs

Haskell

a033292 n k = a033292_tabl !! (n-1) !! (k-1)
a033292_row n = a033292_tabl !! (n-1)
a033292_tabl = f 1 [1..] where
   f k xs = ys : f (k+1) (dropWhile (<= last ys) xs) where
     ys  = take k $ filter ((== 0) . (`mod` 3) . (subtract k)) xs
-- Reinhard Zumkeller, Jan 18 2012 2011

Mathematica

row[n_] := n*(3*n-1)/2 + Range[1, 3*n+1, 3]; Flatten[ Table[ row[n], {n, 0, 11}]] (* Jean-François Alcover, Aug 03 2012 *)

Extensions

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

Offset changed by Reinhard Zumkeller, Jan 18 2012