A045975 Take the first odd integer and multiple of 1, the next 2 even integers and multiples of 2, the next 3 odd integers and multiples of 3, the next 4 even integers and multiples of 4, ...

1, 2, 4, 9, 15, 21, 24, 28, 32, 36, 45, 55, 65, 75, 85, 90, 96, 102, 108, 114, 120, 133, 147, 161, 175, 189, 203, 217, 224, 232, 240, 248, 256, 264, 272, 280, 297, 315, 333, 351, 369, 387, 405, 423, 441, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 561, 583, 605, 627, 649, 671, 693

Offset: 1

Author

Fang-kuo Huang (gsyps(AT)ms17.hinet.net)

Keywords

• nonn
• easy
• nice
• tabl

Comments

A generalized Connell sequence.

Examples

			Triangle begins:
    1;
    2,   4;
    9,  15,  21;
   24,  28,  32,  36;
   45,  55,  65,  75,  85;
   90,  96, 102, 108, 114, 120;
  133, 147, 161, 175, 189, 203, 217;
  ...
		

Links

• Reinhard Zumkeller, Rows n=1..150 of triangle, flattened

Crossrefs

Cf. A001614, A033291.

Seen as a triangle read by rows: cf. A204558 (row sums), A005917 (central terms), A204556 (left edge), A204557 (right edge).

Programs

Haskell

a045975 n k = a045975_tabl !! (n-1) !! (k-1)
a045975_row n = a045975_tabl !! (n-1)
a045975_tabl = f 1 [1..] where
   f k xs = ys : f (k+1) (dropWhile (<= last ys) xs) where
     ys | even k    = take k ms
        | otherwise = take k $ filter odd ms
     ms = filter ((== 0) . (`mod` k)) xs
-- Reinhard Zumkeller, Jan 18 2012

Mathematica

first[n_?EvenQ] := (n - 1)*n^2/2; first[n_?OddQ] := n*(n^2 - 2n + 3)/2; row[n_] := (ro = {first[n]}; next = first[n] + n; While[ Length[ro] < n, If[Mod[next , 2] == Mod[n, 2], AppendTo[ro, next]]; next = next + n]; ro); Flatten[ Table[row[n], {n, 1, 11}]](* Jean-François Alcover, Jun 08 2012 *)

Extensions

More terms from James Sellers

Keyword tabl added by Reinhard Zumkeller, Jan 18 2012