|
%I #18 Jul 02 2017 11:43:24
%S 0,0,1,0,1,2,1,2,2,3,2,3,4,3,4,4,5,4,5,6,5,6,6,7,6,7,8,7,8,8,9,8,9,10,
%T 9,10,10,11,10,11,12,11,12,12,13,12,13,14,13,14,14,15,14,15,16,15,16,
%U 16,17,16,17,18,17,18,18,19,18,19,20,19,20,20,21,20,21,22,21,22,22,23,22,23,24,23,24,24,25,24,25,26,25,26,26,27,26,27,28,27,28,28,29
%N a(n) is the number of odd integers divisible by 7 in ]2*(n-1)^2, 2*n^2[.
%C This sequence has the form (0+2k,0+2k,1+2k,0+2k,1+2k,2+2k,1+2k) for k>=0.
%H Colin Barker, <a href="/A289120/b289120.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F From _Colin Barker_, Jul 02 2017: (Start)
%F G.f.: x^2*(1 + x)*(1 - x + x^2)^2 / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
%F a(n) = a(n-1) + a(n-7) - a(n-8) for n>7.
%F (End)
%t Table[Count[Mod[Table[2 ((n - 1)^2 + k) - 1, {k, 1, 2 n - 1}], 7],
%t 0], {n, 0, 100}]
%o (PARI) concat(vector(2), Vec(x^2*(1 + x)*(1 - x + x^2)^2 / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^100))) \\ _Colin Barker_, Jul 02 2017
%Y Cf. A289133, A289122, A288156, A004523.
%K nonn,easy
%O 0,6
%A _Ralf Steiner_, Jun 25 2017
|
