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

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

Author

Pierre CAMI, May 01 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

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