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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A249349 (A001147(n+1)-1)/2, equals the index of A249348(n) within the triangular numbers A000217.

Original entry on oeis.org

0, 1, 7, 52, 472, 5197, 67567, 1013512, 17229712, 327364537, 6874655287, 158117071612, 3952926790312, 106729023338437, 3095141676814687, 95949391981255312, 3166329935381425312, 110821547738349885937, 4100397266318945779687, 159915493386438885407812
Offset: 0

Views

Author

M. F. Hasler, Oct 26 2014

Keywords

Comments

Also a(n) = floor(sqrt(A249348(n)*2)).
The positive terms are of the form 3k-2; this k (= 1, 3, 18, 157, ...) is the index of A249348(n) within the centered 9-gonal numbers A060544.

Programs

  • PARI
    a(n)=A001147(n+1)\2
  • PARI
    vector(10,n,A001147(n)\2) \\ To get the initial term a(0) for n=1.

Formula

a(n) +(-2*n-3)*a(n-1) +(4*n-1)*a(n-2) +(-2*n+3)*a(n-3)=0. - R. J. Mathar, Oct 28 2014

A249354 a(n) = n*(3*n^2 + 3*n + 1).

Original entry on oeis.org

0, 7, 38, 111, 244, 455, 762, 1183, 1736, 2439, 3310, 4367, 5628, 7111, 8834, 10815, 13072, 15623, 18486, 21679, 25220, 29127, 33418, 38111, 43224, 48775, 54782, 61263, 68236, 75719, 83730, 92287, 101408, 111111, 121414, 132335, 143892, 156103, 168986
Offset: 0

Views

Author

M. F. Hasler, Oct 26 2014

Keywords

Comments

The series Sum a(n)/A007559(n+1)^3 has the sum 1/9 (cf. A249352), analogous to Sum_{n=1..oo} A000217(n)/A001147(n+1)^2 = 1/8 (cf. A249348 and A249349).
Also, nonnegative numbers m such that 9*m + 1 is a cube. - Bruno Berselli, May 23 2017

Links

Crossrefs

Cf. A132355: numbers m such that 9*m + 1 is a square.

Programs

  • Mathematica
    Table[n (3 n^2 + 3 n + 1), {n, 0, 38}] (* or *)
CoefficientList[Series[x (7 + 10 x + x^2)/(x - 1)^4, {x, 0, 38}], x] (* Michael De Vlieger, May 23 2017 *)
  • PARI
    A249354(n)=3*n^3+3*n^2+n

Formula

G.f.: x*(7+10*x+x^2) / (x-1)^4 . - R. J. Mathar, Oct 28 2014
a(n) = n*A003215(n). - R. J. Mathar, Oct 28 2014
Showing 1-2 of 2 results.

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

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