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 1-2 of 2 results.

A143698 12 times hexagonal numbers: 12*n*(2*n-1).

Original entry on oeis.org

0, 12, 72, 180, 336, 540, 792, 1092, 1440, 1836, 2280, 2772, 3312, 3900, 4536, 5220, 5952, 6732, 7560, 8436, 9360, 10332, 11352, 12420, 13536, 14700, 15912, 17172, 18480, 19836, 21240, 22692, 24192, 25740, 27336, 28980, 30672, 32412
Offset: 0

Views

Author

Omar E. Pol, Jan 23 2009

Keywords

Comments

Sequence found by reading the line from 0, in the direction 0, 12,..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818. - Omar E. Pol, Oct 02 2011

Links

Crossrefs

Cf. A000384, A002939, A085250, A094159, A152746, A154617.

Programs

Formula

a(n) = 24*n^2 - 12*n = 12*A000384(n) = 6*A002939(n) = 4*A094159(n) = 3*A085250(n) = 2*A152746(n).
a(n) = a(n-1) + 48*n - 36, with a(0)=0. - Vincenzo Librandi, Dec 14 2010
From G. C. Greubel, May 30 2021: (Start)
G.f.: 12*x*(1 + 3*x)/(1-x)^3.
E.g.f.: 12*x*(1 + 2*x)*exp(x). (End)

A194713 13 times hexagonal numbers: a(n) = 13*n*(2*n-1).

Original entry on oeis.org

0, 13, 78, 195, 364, 585, 858, 1183, 1560, 1989, 2470, 3003, 3588, 4225, 4914, 5655, 6448, 7293, 8190, 9139, 10140, 11193, 12298, 13455, 14664, 15925, 17238, 18603, 20020, 21489, 23010, 24583, 26208, 27885, 29614, 31395, 33228, 35113, 37050, 39039, 41080, 43173
Offset: 0

Views

Author

Omar E. Pol, Oct 02 2011

Keywords

Comments

Sequence found by reading the line from 0, in the direction 0, 13, ..., in the square spiral whose vertices are the generalized 15-gonal numbers.

Links

Crossrefs

Cf. A000384, A002939, A094159, A143698, A152745, A154617, A195320.

Programs

Formula

a(n) = 26*n^2 - 13*n = 13*A000384(n).
a(n) = a(n-1) + 52*n - 39, a(0)=0. - Vincenzo Librandi, Oct 03 2011
From Elmo R. Oliveira, Dec 15 2024: (Start)
G.f.: 13*x*(1 + 3*x)/(1 - x)^3.
E.g.f.: 13*x*(1 + 2*x)*exp(x).
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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