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.

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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

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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

A136392 a(n) = 6*n^2 - 10*n + 5.

Original entry on oeis.org

1, 9, 29, 61, 105, 161, 229, 309, 401, 505, 621, 749, 889, 1041, 1205, 1381, 1569, 1769, 1981, 2205, 2441, 2689, 2949, 3221, 3505, 3801, 4109, 4429, 4761, 5105, 5461, 5829, 6209, 6601, 7005, 7421, 7849, 8289, 8741, 9205, 9681, 10169, 10669, 11181, 11705, 12241
Offset: 1

Views

Author

Gary W. Adamson, Dec 28 2007

Keywords

Comments

Binomial transform of [1, 8, 12, 0, 0, 0, ...].
Numbers k such that 6*k - 5 is the square of a number of the form 6*k - 5, contained in A199859. - Eleonora Echeverri-Toro, Nov 29 2011
Central terms of the triangle A033292. - Reinhard Zumkeller, Feb 06 2012
Sequence found by reading the line from 1, in the direction 1, 9, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Jul 18 2012

Links

Crossrefs

Cf. A000567, A001318, A016777, A033292, A033580, A059722, A199859, A201279, A204675.

Programs

Formula

a(n) = n*(3*n - 2) + (n-1)*(3*n - 5), n > 1.
a(n) = n*A016777(n-1) + (n-1)*A016777(n-2).
a(n) = a(n-1) + 12*n - 16 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010
G.f.: x*(1+x)*(1+5*x)/(1-x)^3. - Colin Barker, Jan 09 2012
a(n) = 1 + A033580(n-1). - Omar E. Pol, Jul 18 2012
a(n) = A059722(n) - A059722(n-1). - J. M. Bergot, Nov 02 2012
a(n) = A000567(n-1) + A000567(n). - Charlie Marion, May 29 2024
From Elmo R. Oliveira, Oct 31 2024: (Start)
E.g.f.: exp(x)*(2*x*(3*x - 2) + 5) - 5.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
Showing 1-2 of 2 results.

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

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