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

Author

N. J. A. Sloane, Aug 23 2009

Keywords

• nonn
• easy

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).

Programs

Magma

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

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

Extensions

Definition rewritten by Bruno Berselli, Sep 29 2011