A151978 - OEIS

%I #31 Sep 08 2022 08:45:38

%S 0,1,17,18,34,35,51,52,68,69,85,86,102,103,119,120,136,137,153,154,

%T 170,171,187,188,204,205,221,222,238,239,255,256,272,273,289,290,306,

%U 307,323,324,340,341,357,358,374,375,391,392,408,409,425,426,442,443,459,460,476

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

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

%H Vincenzo Librandi, <a href="/A151978/b151978.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F From _Bruno Berselli_, Sep 29 2011: (Start)

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

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

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

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

%F 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

%t 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 *)

%o (Magma) [n: n in [0..30] | n mod 17 in [0,1]]; // _Bruno Berselli_, Sep 29 2011

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Aug 23 2009

%E Definition rewritten by _Bruno Berselli_, Sep 29 2011