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.

A106389 Numbers j such that 6j^2 + 6j + 1 = 13k.

Original entry on oeis.org

1, 11, 14, 24, 27, 37, 40, 50, 53, 63, 66, 76, 79, 89, 92, 102, 105, 115, 118, 128, 131, 141, 144, 154, 157, 167, 170, 180, 183, 193, 196, 206, 209, 219, 222, 232, 235, 245, 248, 258, 261, 271, 274, 284, 287, 297, 300, 310, 313, 323, 326, 336, 339, 349, 352
Offset: 1

Views

Author

Pierre CAMI, May 01 2005

Keywords

Links

Crossrefs

Cf. A106387, A106388, A106390.
For k sequence see A106390.

Programs

  • Mathematica
    fQ[n_] := IntegerQ[(6n(n + 1) + 1)/13]; Select[ Range[ 361], fQ[ # ] &] (* Robert G. Wilson v, May 02 2005 *)
LinearRecurrence[{1,1,-1},{1,11,14},60] (* Harvey P. Dale, Jun 07 2016 *)
  • PARI
    Vec((2*x^2+10*x+1)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Apr 16 2014

Formula

j(1)=1, j(2)=11; then j(n)=j(n-2)+13.
a(n) = (-15+7*(-1)^n+26*n)/4. G.f.: x*(2*x^2+10*x+1) / ((x-1)^2*(x+1)). - Colin Barker, Apr 16 2014

Extensions

More terms from Robert G. Wilson v, May 02 2005

A106388 Numbers k such that 11k = 6j^2 + 6j + 1.

Original entry on oeis.org

11, 23, 131, 167, 383, 443, 767, 851, 1283, 1391, 1931, 2063, 2711, 2867, 3623, 3803, 4667, 4871, 5843, 6071, 7151, 7403, 8591, 8867, 10163, 10463, 11867, 12191, 13703, 14051, 15671, 16043, 17771, 18167, 20003, 20423, 22367, 22811, 24863, 25331, 27491, 27983
Offset: 1

Views

Author

Pierre CAMI, May 01 2005

Keywords

Comments

j sequence = A106387

Links

Crossrefs

Cf. A106387, A106389, A106390.

Programs

  • Mathematica
    LinearRecurrence[{1,2,-2,-1,1},{11,23,131,167,383},50] (* Harvey P. Dale, Jul 26 2018 *)
  • PARI
    Vec((11+12*x+86*x^2+12*x^3+11*x^4)/(1+x)^2/(1-x)^3+O(x^99)) \\ Charles R Greathouse IV, Dec 28 2011

Formula

a(1)=11, a(2)=23; if n odd a(n)=a(n-1)+54*(n-1), if n even a(n)=a(n-1)+12*(n-1).
a(n) = (66*n*(n-1)-21*(2*n-1)*(-1)^n+23)/4.
G.f.: x*(11+12*x+86*x^2+12*x^3+11*x^4)/((1+x)^2*(1-x)^3).
a(n)-a(n-1)-2*a(n-2)+2*a(n-3)+a(n-4)-a(n-5) = 0 for n>5.

Extensions

Formulae corrected and added by Bruno Berselli, Nov 16 2010
More terms from Colin Barker, Apr 16 2014

A106390 Numbers k such that 13k = 6j^2 + 6j + 1.

Original entry on oeis.org

1, 61, 97, 277, 349, 649, 757, 1177, 1321, 1861, 2041, 2701, 2917, 3697, 3949, 4849, 5137, 6157, 6481, 7621, 7981, 9241, 9637, 11017, 11449, 12949, 13417, 15037, 15541, 17281, 17821, 19681, 20257, 22237, 22849, 24949, 25597, 27817, 28501, 30841
Offset: 1

Views

Author

Pierre CAMI, May 01 2005

Keywords

Links

Crossrefs

Cf. A106387, A106388, A106389.
For j sequence see A106389.

Programs

  • Mathematica
    f[n_] := Block[{k = (6n(n + 1) + 1)/13}, If[ IntegerQ[k], k, 1]]; Union[ Table[ f[n], {n, 270}]] (* Robert G. Wilson v, May 02 2005 *)
  • PARI
    Vec(-x*(x^4+60*x^3+34*x^2+60*x+1)/((x-1)^3*(x+1)^2) + O(x^100)) \\ Colin Barker, Apr 16 2014

Formula

a(1)=1, a(2)=61; for odd n a(n) = a(n-1)+18*(n-1), for even n a(n) = a(n-1)+60*(n-1).
a(n) = (25-21*(-1)^n+6*(-13+7*(-1)^n)*n+78*n^2)/4. - Colin Barker, Apr 16 2014
G.f.: -x*(x^4+60*x^3+34*x^2+60*x+1) / ((x-1)^3*(x+1)^2). - Colin Barker, Apr 16 2014

Extensions

More terms from Robert G. Wilson v, May 02 2005
Showing 1-3 of 3 results.

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