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A112652 a(n) squared is congruent to a(n) (mod 12). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

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).

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)

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

Cf. A000217, A087960.

Sequence in context: A069219 A312848 A010413 * A272933 A243650 A140399

Adjacent sequences:  A112649 A112650 A112651 * A112653 A112654 A112655

KEYWORD

nonn,easy

AUTHOR

Jeremy Gardiner, Dec 28 2005

STATUS

approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)