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A151971 Numbers n such that n^2 - n is divisible by 21. 3
0, 1, 7, 15, 21, 22, 28, 36, 42, 43, 49, 57, 63, 64, 70, 78, 84, 85, 91, 99, 105, 106, 112, 120, 126, 127, 133, 141, 147, 148, 154, 162, 168, 169, 175, 183, 189, 190, 196, 204, 210, 211, 217, 225, 231, 232, 238, 246, 252, 253, 259, 267, 273, 274, 280, 288, 294, 295, 301, 309 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equivalently, numbers that are congruent to {0, 1, 7, 15} mod 21. - Bruno Berselli, Aug 06 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

From Bruno Berselli, Aug 06 2012: (Start)

G.f.: x^2*(1+6*x+8*x^2+6*x^3)/((1+x)*(1-x)^2*(1+x^2)).

a(n) = (42*n +14*i^((n-1)*n) -3*(-1)^n -3)/8 -7, where i=sqrt(-1). (End)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Wesley Ivan Hurt, Jun 07 2016

E.g.f.: (24 + (21*x - 31)*cosh(x) + 7*(sin(x) + cos(x) + (3*x - 4)*sinh(x)))/4. - Ilya Gutkovskiy, Jun 07 2016

MAPLE

A151971:=n->(42*n+14*I^((n-1)*n)-3*I^(2*n)-3)/8-7: seq(A151971(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

MATHEMATICA

Select[Range[0, 400], Divisible[#^2-#, 21]&] (* Harvey P. Dale, Jun 04 2012 *)

PROG

(MAGMA) [n: n in [0..309] | IsZero((n^2-n) mod 21)]; // Bruno Berselli, Aug 06 2012

(Maxima) makelist((42*n+14*%i^((n-1)*n)-3*(-1)^n-3)/8-7, n, 1, 60); /* Bruno Berselli, Aug 06 2012 */

CROSSREFS

For m^2 == m (mod n), see: n=2: A001477; n=3: A032766; n=4: A042948; n=5: A008851; n=6: A032766; n=7: A047274; n=8: A047393; n=9: A090570; n=10: A008851; n=11: A112651; n=12: A112652; n=13:A112653; n=14: A047274; n=15: A151972; n=16: A151977; n=17: A151978; n=18: A090570; n=19: A151979; n=20: A151980; n=21: A151971; n=22: A112651; n=24: A151973; n=26: A112653; n=30: A151972; n=32: A151983; n=34: A151978; n=38: A151979; n=42: A151971; n=48: A151981; n=64: A151984.

Cf. A215202.

Sequence in context: A140109 A064397 A214467 * A014659 A179676 A053354

Adjacent sequences:  A151968 A151969 A151970 * A151972 A151973 A151974

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 23 2009

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)