A289120 a(n) is the number of odd integers divisible by 7 in ]2*(n-1)^2, 2*n^2[.

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, 9, 10, 10, 11, 10, 11, 12, 11, 12, 12, 13, 12, 13, 14, 13, 14, 14, 15, 14, 15, 16, 15, 16, 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

Offset

0,6

Comments

This sequence has the form (0+2k,0+2k,1+2k,0+2k,1+2k,2+2k,1+2k) for k>=0.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

From Colin Barker, Jul 02 2017: (Start)

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)).

a(n) = a(n-1) + a(n-7) - a(n-8) for n>7.

(End)

Mathematica

Table[Count[Mod[Table[2 ((n - 1)^2 + k) - 1, {k, 1, 2 n - 1}], 7],
  0], {n, 0, 100}]

Prog

(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

Crossrefs

Cf. A289133, A289122, A288156, A004523.

Sequence in context: A029263 A097575 A103273 * A025066 A060426 A260412

Adjacent sequences: A289117 A289118 A289119 * A289121 A289122 A289123

Keyword

nonn,easy

Author

Ralf Steiner, Jun 25 2017

Status

approved