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.

A112414 a(n) = 3*n + 7.

Original entry on oeis.org

7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 178, 181, 184
Offset: 0

Views

Author

Zerinvary Lajos, Dec 09 2005

Keywords

Comments

At least the first 2 million terms from a(1) on coincide with the corresponding terms of A086822(n+2). - R. J. Mathar, Aug 15 2008

Links

Crossrefs

Cf. A016933, A059845.

Programs

Formula

From Elmo R. Oliveira, Oct 30 2024: (Start)
G.f.: (7 - 4*x)/(1 - x)^2.
E.g.f.: (7 + 3*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2.
a(n) = A016933(n+2)/2 = A059845(n+1) - A059845(n). (End)

Extensions

Better definition from T. D. Noe, Nov 30 2006

A085899 a(n) = floor( 2*(1 + n + 2*n^2 + 4*n^3)/(1 + 2*n + n^2)).

Original entry on oeis.org

4, 9, 16, 23, 30, 38, 46, 53, 61, 69, 77, 85, 93, 101, 109, 117, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 308, 316, 324, 332, 340, 348, 356, 364, 372, 380, 388
Offset: 1

Views

Author

Wang Dan (wangdan01(AT)lycos.com), Aug 15 2003

Keywords

Examples

			a(2) = floor(2*(1*2^0+1*2^1+2*2^2+4*2^3)/(1*2^0+2*2^1+1*2^2)) = floor(2*43/9) = floor(9.55556) = 9.

Crossrefs

Cf. A086790, A086814, A086822.

Programs

  • Mathematica
    Table[Floor[(2(1+n+2n^2+4n^3))/(1+2n+n^2)],{n,50}] (* Harvey P. Dale, Apr 01 2018 *)
  • PARI
    a(n) = floor(2*((1 + n + 2*n^2 + 4*n^3)/(1 + 2*n + n^2))); \\ Michel Marcus, Aug 31 2013

Extensions

Definition corrected by Michel Marcus, Aug 31 2013

A085505 a(n) = ceiling(((1*n^0 + 1*n^1 + 2*n^2 + 4*n^3)/(1*n^0 + 2*n^1 + 1*n^2))^2).

Original entry on oeis.org

4, 23, 67, 138, 239, 371, 534, 728, 954, 1212, 1501, 1822, 2175, 2560, 2977, 3425, 3906, 4419, 4963, 5539, 6148, 6788, 7461, 8165, 8901, 9669, 10470, 11302, 12166, 13062, 13990, 14951, 15943, 16967, 18023, 19111, 20231, 21384, 22568
Offset: 1

Views

Author

Wang Dan (wangdan01(AT)lycos.com), Aug 19 2003

Keywords

Crossrefs

Cf. A085899, A086790, A086814, A086822.

Programs

  • Mathematica
    Table[Ceiling[((1+n+2n^2+4n^3)/(1+2n+n^2))^2],{n,40}] (* Harvey P. Dale, Jun 14 2011 *)

Extensions

Corrected by M. F. Hasler, Jul 23 2007
Showing 1-3 of 3 results.

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

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