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A033291 A Connell-like sequence: take the first multiple of 1, the next 2 multiples of 2, the next 3 multiples of 3, etc. 6
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Reinhard Zumkeller, Rows n = 1..100, flattened

Gary E. Stevens, A Connell-Like Sequence, J. Integer Sequences, 1 (1998), #98.1.4.

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)))).

EXAMPLE

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; ...

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-Fran├žois Alcover, Sep 30 2011 *)

PROG

(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

(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

CROSSREFS

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

Cf. A045975, A033292, A033293.

Sequence in context: A053096 A155752 A145801 * A105434 A145196 A061536

Adjacent sequences:  A033288 A033289 A033290 * A033292 A033293 A033294

KEYWORD

nonn,easy,nice,tabl

AUTHOR

Gary E. Stevens

EXTENSIONS

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

STATUS

approved

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Last modified July 26 10:48 EDT 2021. Contains 346294 sequences. (Running on oeis4.)