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.

Showing 1-3 of 3 results.

A022289 a(n) = n*(31*n + 1)/2.

Original entry on oeis.org

0, 16, 63, 141, 250, 390, 561, 763, 996, 1260, 1555, 1881, 2238, 2626, 3045, 3495, 3976, 4488, 5031, 5605, 6210, 6846, 7513, 8211, 8940, 9700, 10491, 11313, 12166, 13050, 13965, 14911, 15888, 16896, 17935
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. similar sequences of the form n*((2*k+1)*n + 1)/2: A000217 (k=0), A005449 (k=1), A005475 (k=2), A022265 (k=3), A022267 (k=4), A022269 (k=5), A022271 (k=6), A022273 (k=7), A022275 (k=8), A022277 (k=9), A022279 (k=10), A022281 (k=11), A022283 (k=12), A022285 (k=13), A022287 (k=14), this sequence (k=15).

Programs

Formula

a(n) = 31*n + a(n-1) - 15, for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
G.f.: x*(16 + 15*x)/(1 - x)^3 . - R. J. Mathar, Sep 02 2016
a(n) = A000217(16*n) - A000217(15*n). In general, n*((2*k+1)*n + 1)/2 = A000217((k+1)*n) - A000217(k*n). - Bruno Berselli, Oct 13 2016
E.g.f.: (x/2)*(31*x + 32)*exp(x). - G. C. Greubel, Aug 23 2017

A022268 a(n) = n*(11*n - 1)/2.

Original entry on oeis.org

0, 5, 21, 48, 86, 135, 195, 266, 348, 441, 545, 660, 786, 923, 1071, 1230, 1400, 1581, 1773, 1976, 2190, 2415, 2651, 2898, 3156, 3425, 3705, 3996, 4298, 4611, 4935, 5270, 5616, 5973, 6341, 6720, 7110, 7511, 7923, 8346, 8780, 9225, 9681, 10148, 10626, 11115
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of sets with two elements that can be obtained by selecting distinct elements from two sets with 2n and 3n elements respectively and n common elements. - Polina S. Dolmatova (polinasport(AT)mail.ru), Jul 11 2003

Links

Crossrefs

Cf. A000217, A022281.
Cf. index to sequence with numbers of the form n*(d*n+10-d)/2 in A140090.
Cf. similar sequences listed in A022288.

Programs

Formula

G.f.: x*(5 + 6*x)/(1-x)^3. - Bruno Berselli, Feb 11 2011
a(n) = 11*n + a(n-1) - 6 for n>0. - Vincenzo Librandi, Aug 04 2010
a(n) = A000217(6*n-1) - A000217(5*n-1). - Bruno Berselli, Oct 17 2016
From Wesley Ivan Hurt, Dec 04 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
a(n) = (1/9) * Sum_{i=n..10n-1} i. (End)
E.g.f.: (1/2)*(11*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 17 2017

A022280 a(n) = n*(23*n - 1)/2.

Original entry on oeis.org

0, 11, 45, 102, 182, 285, 411, 560, 732, 927, 1145, 1386, 1650, 1937, 2247, 2580, 2936, 3315, 3717, 4142, 4590, 5061, 5555, 6072, 6612, 7175, 7761, 8370, 9002, 9657, 10335, 11036, 11760, 12507, 13277
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A000217, A022281.
Cf. similar sequences listed in A022288.

Programs

Formula

a(n) = 23*n + a(n-1) - 12 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
From Colin Barker, Jun 05 2012: (Start)
G.f.: x*(11 + 12*x)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
a(n) = A000217(12*n-1) - A000217(11*n-1). - Bruno Berselli, Oct 14 2016
E.g.f.: (x/2)*(23*x + 22)*exp(x). - G. C. Greubel, Aug 23 2017
Showing 1-3 of 3 results.

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

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