A112652 a(n) squared is congruent to a(n) (mod 12).

0, 1, 4, 9, 12, 13, 16, 21, 24, 25, 28, 33, 36, 37, 40, 45, 48, 49, 52, 57, 60, 61, 64, 69, 72, 73, 76, 81, 84, 85, 88, 93, 96, 97, 100, 105, 108, 109, 112, 117, 120, 121, 124, 129, 132, 133, 136, 141, 144, 145, 148, 153, 156, 157, 160, 165, 168, 169, 172, 177, 180

Offset: 0

Author

Jeremy Gardiner, Dec 28 2005

Keywords

• nonn
• easy

Comments

Numbers m such that A000217(3*m)/2 + A000217(2*m)/3 is an integer. - Bruno Berselli, Jul 01 2016

Examples

			a(3) = 9 because 9^2 = 81 = 6*12 + 9, hence 81 == 9 (mod 12).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Crossrefs

Cf. A000217, A087960.

Programs

Maple

m = 12 for n = 1 to 300 if n^2 mod m = n mod m then print n; next n

Mathematica

Select[Range[0, 180], Mod[#^2, 12] == Mod[#, 12] &] (* or *)
CoefficientList[Series[x (1 + 2 x + 3 x^2)/((x^2 + 1) (x - 1)^2), {x, 0, 60}], x] (* Michael De Vlieger, Jul 01 2016 *)

PARI

is(n)=(n^2-n)%12==0 \\ Charles R Greathouse IV, Oct 16 2015

Formula

From R. J. Mathar, Sep 25 2009: (Start)

G.f.: x*(1 + 2*x + 3*x^2)/((x^2 + 1)*(x - 1)^2).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4).

a(n) = A087960(n) + 3*n - 1. (End)