A151978 Numbers that are congruent to {0, 1} mod 17.

0, 1, 17, 18, 34, 35, 51, 52, 68, 69, 85, 86, 102, 103, 119, 120, 136, 137, 153, 154, 170, 171, 187, 188, 204, 205, 221, 222, 238, 239, 255, 256, 272, 273, 289, 290, 306, 307, 323, 324, 340, 341, 357, 358, 374, 375, 391, 392, 408, 409, 425, 426, 442, 443, 459, 460, 476

Offset

1,3

Comments

Numbers n such that n^2 - n is divisible by 17.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

From Bruno Berselli, Sep 29 2011: (Start)

G.f.: x^2*(1+16*x)/((1+x)*(1-x)^2).

a(n) = (34*n - 15*(-1)^n - 49)/4.

a(n) = a(n-1) + a(n-2) - a(n-3) = a(n-2) + 17.

a(n) + a(n+1) = a(2n). (End)

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1 and b(k) = 17*2^(k-1) for k > 0. - Philippe Deléham, Oct 19 2011

Mathematica

LinearRecurrence[{1, 1, -1}, {0, 1, 17}, 60] (* or *) With[{c=17Range[0, 30]}, Sort[Join[c, c+1]]] (* Harvey P. Dale, Oct 04 2011 *)

Prog

(Magma) [n: n in [0..30] | n mod 17 in [0, 1]]; // Bruno Berselli, Sep 29 2011

Crossrefs

Sequence in context: A018821 A255923 A226673 * A111054 A242975 A155561

Adjacent sequences: A151975 A151976 A151977 * A151979 A151980 A151981

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 23 2009

Extensions

Definition rewritten by Bruno Berselli, Sep 29 2011

Status

approved