A033291 A Connell-like sequence: take the first multiple of 1, the next 2 multiples of 2, the next 3 multiples of 3, etc.

1, 2, 4, 6, 9, 12, 16, 20, 24, 28, 30, 35, 40, 45, 50, 54, 60, 66, 72, 78, 84, 91, 98, 105, 112, 119, 126, 133, 136, 144, 152, 160, 168, 176, 184, 192, 198, 207, 216, 225, 234, 243, 252, 261, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 374, 385, 396, 407, 418, 429, 440, 451, 462

Offset: 1

Author

Gary E. Stevens

Keywords

• nonn
• easy
• nice
• tabl

Comments

Row sums are 0, 1, 6, 27, 88, 200, ... with g.f. -x*(1 + 4*x + 16*x^2 + 37*x^3 + 39*x^4 + 54*x^5 + 39*x^6 + 17*x^7 + 8*x^8 + x^9) / ( (1 + x + x^2)^3*(x-1)^5 ). - R. J. Mathar, Aug 10 2017

Examples

			Triangle begins
   1;
   2,  4;
   6,  9,  12;
  16, 20,  24,  28;
  30, 35,  40,  45,  50;
  54, 60,  66,  72,  78,  84;
  91, 98, 105, 112, 119, 126, 133; ...
		

Links

• Reinhard Zumkeller, Rows n = 1..100, flattened
• Gary E. Stevens, A Connell-Like Sequence, J. Integer Sequences, 1 (1998), #98.1.4.

Crossrefs

Cf. A192735 (left edge), A192736 (right edge).

Cf. A045975, A033292, A033293.

Programs

Haskell

a033291 n k = a033291_tabl !! (n-1) !! (k-1)
a033291_row n = a033291_tabl !! (n-1)
a033291_tabl = f 1 [1..] where
   f k xs = ys : f (k+1) (dropWhile (<= last ys) xs) where
     ys  = take k $ filter ((== 0) . (`mod` k)) xs
a192735 n = head $ a033291_tabl !! (n-1)
a192736 n = last $ a033291_tabl !! (n-1)
-- Reinhard Zumkeller, Jan 18 2012, Jul 08 2011

Maple

A033291 := proc(n,k)
    A192735(n)+(k-1)*n ;
end proc:
seq(seq(A033291(n,k),k=1..n),n=1..10) ; # R. J. Mathar, Aug 10 2017

Mathematica

Flatten[ Table[ n*(Floor[ (n-1)^2/3] + k), {n, 1, 12}, {k, 1, n}]] (* Jean-François Alcover, Sep 30 2011 *)

PARI

a(n)=my(q=(sqrtint(8*n-7)+1)\2); q*n-q*(q+1)\6*q \\ Charles R Greathouse IV, Jan 06 2016

Formula

a(n) = q(n)*n - q(n)*floor(q(n)*(q(n)+1)/6) with q(n) = ceiling((1/2)*(-1 + sqrt(1+8*(n)))).

Extensions

Corrected and formula added by Johannes W. Meijer, Oct 07 2010