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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A153875 3 times 13-gonal (or tridecagonal) numbers: a(n) = 3*n*(11*n - 9)/2.

Original entry on oeis.org

0, 3, 39, 108, 210, 345, 513, 714, 948, 1215, 1515, 1848, 2214, 2613, 3045, 3510, 4008, 4539, 5103, 5700, 6330, 6993, 7689, 8418, 9180, 9975, 10803, 11664, 12558, 13485, 14445, 15438, 16464, 17523, 18615, 19740, 20898, 22089
Offset: 0

Views

Author

Omar E. Pol, Jan 03 2009

Keywords

Links

Crossrefs

Cf. A051865, A152997.
3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153783, A153448.
Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=33: see Comments lines of A226492.

Programs

Formula

a(n) = (33*n^2 - 27*n)/2 = A051865(n)*3.
a(n) = a(n-1) + 33*n - 30, with n>0, a(0)=0. - Vincenzo Librandi, Dec 14 2010
G.f.: 3*x*(1 + 10*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011
From G. C. Greubel, Aug 31 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: (3/2)*x*(2 + 11*x)*exp(x). (End)

A152760 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).

Original entry on oeis.org

0, 4, 36, 96, 184, 300, 444, 616, 816, 1044, 1300, 1584, 1896, 2236, 2604, 3000, 3424, 3876, 4356, 4864, 5400, 5964, 6556, 7176, 7824, 8500, 9204, 9936, 10696, 11484, 12300, 13144, 14016, 14916, 15844, 16800, 17784, 18796, 19836, 20904, 22000, 23124
Offset: 0

Views

Author

Omar E. Pol, Dec 14 2008

Keywords

Comments

Sequence found by reading the line from 0, in the direction 0, 4, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. The square spiral is related to the primitive Pythagorean triple [3, 4, 5]. - Omar E. Pol, Oct 13 2011

Links

Crossrefs

Cf. A001106, A139268, A152759, A195019, A195020, A195021.

Programs

Formula

a(n) = 14*n^2 - 10*n = 4*A001106(n) = 2*A139268(n).
a(n) = a(n-1) + 28*n - 24 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
From Colin Barker, Apr 09 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 4*x*(1+6*x)/(1-x)^3. (End)
From Elmo R. Oliveira, Dec 27 2024: (Start)
E.g.f.: 2*exp(x)*x*(2 + 7*x).
a(n) = n + A195021(n). (End)
Previous Showing 11-12 of 12 results.

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

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