A192735 -id:A192735 - cp's OEIS frontend

A087483 Row 0 of the order array of 3/2, i.e., row 0 of the transposable dispersion in A087465.

1, 2, 4, 6, 9, 13, 17, 22, 28, 34, 41, 49, 57, 66, 76, 86, 97, 109, 121, 134, 148, 162, 177, 193, 209, 226, 244, 262, 281, 301, 321, 342, 364, 386, 409, 433, 457, 482, 508, 534, 561, 589, 617, 646, 676, 706, 737, 769, 801, 834, 868, 902, 937, 973, 1009, 1046, 1084

Offset: 0

Clark Kimberling, Sep 09 2003

Also, column 0 of the transposable dispersion in A087468.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs. 7 (2004), article 04.1.6.
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Cf. A053799, A087465, A087468.

A087483 := proc(n)
    1+floor((n+1)^2/3) ;
end proc:
seq(A087483(n),n=0..10) ; # R. J. Mathar, Aug 10 2017

LinearRecurrence[{2, -1, 1, -2, 1}, {1, 2, 4, 6, 9}, 100] (* Jean-François Alcover, Mar 29 2020 *)

a(n) = n + 1 - floor(n/3) + Sum_{i=1..n} floor(2i/3).
a(n) = 1 + floor((n+1)^2/3) = 1 + A000212(n+1).
a(n) = A192735(n+2) / (n+2). - Reinhard Zumkeller, Jul 08 2011
G.f.: -(x^4-x^3+x^2+1) / ((x-1)^3*(x^2+x+1)). - Colin Barker, Mar 31 2013

Edited by Max Alekseyev, Dec 05 2013

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

Original entry on oeis.org

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

Gary E. Stevens

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

			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; ...

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

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

Cf. A045975, A033292, A033293.

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

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

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

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

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)))).

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

A192736 Right edge of the triangle in A033291.

Original entry on oeis.org

1, 4, 12, 28, 50, 84, 133, 192, 270, 370, 484, 624, 793, 980, 1200, 1456, 1734, 2052, 2413, 2800, 3234, 3718, 4232, 4800, 5425, 6084, 6804, 7588, 8410, 9300, 10261, 11264, 12342, 13498, 14700, 15984, 17353, 18772, 20280, 21880, 23534, 25284, 27133, 29040

Offset: 1

Reinhard Zumkeller, Jul 08 2011

nonn

a(n) = A007980(n-1) * n.

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Cf. A192735.

Haskell
```
See A033291.
```

G.f.: x*(2*x^5+2*x^4+6*x^3+5*x^2+2*x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Mar 31 2013

cp's OEIS Frontend

A087483 Row 0 of the order array of 3/2, i.e., row 0 of the transposable dispersion in A087465.

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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.

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A192736 Right edge of the triangle in A033291.

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