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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A181485 Indices of records in A171919 = number of solutions to n=x*y*z, x+y=z+1.

Original entry on oeis.org

1, 4, 112, 144, 23400, 28224, 247104, 604800, 26812800, 2677752000, 6805814400, 165145780800, 1248124550400, 17996854730400, 388778796252000
Offset: 1

Views

Author

R. J. Mathar and M. F. Hasler, Oct 23 2010

Keywords

Comments

The sequence lists all n such that A171919(n) > A171919(k) for all k < n.
Also the subsequence of terms of A171920 for which A171919 is larger than for all preceding values.
The actual record values are given in A181486.
a(10) > 5*10^7.
It seems highly probable that all terms of this sequence, except for a(1) = 1, are multiples of 4.
a(14) > 4*10^12. - Donovan Johnson, Jun 14 2011
a(16) > 2*10^17. - Robert Gerbicz, Apr 10 2012

Examples

			a(1) = 1 since there is no smaller value possible.
a(2) = 4 is the smallest number for which there are more than 1 = A171919(1) solutions to n = x*y*z, x + y = z + 1.
a(3) = 112 is the smallest number for which there are more than 2 = A171919(4) solutions to n = x*y*z, x + y = z + 1.

Programs

  • PARI
    m=0;for(n=1,1e9,A171919(n)>m | next; m=A171919(n); print1(n", "))

Extensions

a(10)-a(13) from Donovan Johnson, Jun 14 2011
a(14)-a(15) from Robert Gerbicz, Apr 10 2012

A241496 Expansion of (1 + 4*x + x^2) / (1 - x^2)^3.

Original entry on oeis.org

1, 4, 4, 12, 9, 24, 16, 40, 25, 60, 36, 84, 49, 112, 64, 144, 81, 180, 100, 220, 121, 264, 144, 312, 169, 364, 196, 420, 225, 480, 256, 544, 289, 612, 324, 684, 361, 760, 400, 840, 441, 924, 484, 1012, 529, 1104, 576, 1200, 625, 1300, 676, 1404, 729, 1512
Offset: 0

Views

Author

Stefano Maruelli, Apr 24 2014

Keywords

Comments

Column 3 of the table in A229834.

Links

Crossrefs

Cf. A001082, A229834.
Cf. A171920: a(2k) = A000290(k+1); A046092: a(2k+1)= A046092(k+1).

Programs

  • Mathematica
    Table[(3 n (n + 4) - (-1)^n (n (n + 4) + 2) + 10)/8, {n, 0, 60}] (* Bruno Berselli, Apr 24 2014 *)
LinearRecurrence[{0,3,0,-3,0,1},{1,4,4,12,9,24},60] (* Harvey P. Dale, Nov 25 2016 *)

Formula

G.f.: (1 + 4*x + x^2) / (1 - x^2)^3. [Bruno Berselli, Apr 24 2014]
a(n) = a(-n-4) = 1 + ( 3*n*(n + 4) + 2 - (-1)^n*(n*(n + 4) + 2) )/8. [Bruno Berselli, Apr 24 2014]

Extensions

Edited by Bruno Berselli, Apr 24 2014
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