cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Gary E. Stevens

Gary E. Stevens's wiki page.

Gary E. Stevens has authored 3 sequences.

A033293 A Connell-like sequence: take 1 number = 1 (mod Q), 2 numbers = 2 (mod Q), 3 numbers = 3 (mod Q), etc., where Q = 8.

Original entry on oeis.org

1, 2, 10, 11, 19, 27, 28, 36, 44, 52, 53, 61, 69, 77, 85, 86, 94, 102, 110, 118, 126, 127, 135, 143, 151, 159, 167, 175, 176, 184, 192, 200, 208, 216, 224, 232, 233, 241, 249, 257, 265, 273, 281, 289, 297, 298, 306, 314, 322, 330, 338, 346, 354, 362, 370, 371, 379, 387, 395, 403, 411
Offset: 1

Views

Author

Gary E. Stevens

Keywords

Links

Crossrefs

Cf. A054552 (left edge), A001107 (right edge), A204674 (row sums), A204675 (central terms).

Programs

  • Haskell
    a033293 n k = a033293_tabl !! (n-1) !! (k-1)
a033293_row n = a033293_tabl !! (n-1)
a033293_tabl = f 1 [1..] where
   f k xs = ys : f (k+1) (dropWhile (<= last ys) xs) where
     ys  = take k $ filter ((== 0) . (`mod` 8) . (subtract k)) xs
-- Reinhard Zumkeller, Jan 18 2012 2011
  • Mathematica
    row[1] = {1}; row[n_] := row[n] = Table[row[n-1][[-1]] + 8k + 1, {k, 0, n-1}]; Table[row[n], {n, 1, 11}] // Flatten (* Jean-François Alcover, Jan 25 2013 *)

Extensions

More terms from jeroen.lahousse(AT)icl.com
Offset changed by Reinhard Zumkeller, Jan 18 2012

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

Views

Author

Gary E. Stevens

Keywords

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

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

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.

Original entry on oeis.org

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

Views

Author

Gary E. Stevens

Keywords

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

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.