A289139 a(n) is the number of odd integers divisible by 7 in ]4*(n-1)^2, 4*n^2[.

0, 0, 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 10, 11, 12, 12, 13, 14, 14, 14, 15, 16, 16, 17, 18, 18, 18, 19, 20, 20, 21, 22, 22, 22, 23, 24, 24, 25, 26, 26, 26, 27, 28, 28, 29, 30, 30, 30, 31, 32, 32, 33, 34, 34, 34, 35, 36, 36, 37, 38, 38, 38, 39, 40, 40

Offset: 0

Author

Ralf Steiner, Jun 26 2017

Keywords

• nonn
• easy

Comments

This sequence has the form (0+4k,0+4k,1+4k,2+4k,2+4k,2+4k,3+4k) for k>=0.

Links

• Harvey P. Dale, 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).

Crossrefs

Cf. A289120, A289133, A289122, A288156, A004523.

Programs

Mathematica

Table[Count[Mod[Table[2(2(n-1)^2 +k)-1, {k,1,4 n-2}],7],0], {n,0,100}]
LinearRecurrence[{1,0,0,0,0,0,1,-1},{0,0,1,2,2,2,3,4},80] (* Harvey P. Dale, Aug 10 2025 *)

Formula

a(n + 7*k) = a(n) + 4*k.

G.f.: (x^7+x^6+x^3+x^2)/(x^8-x^7-x+1). - Alois P. Heinz, Jun 26 2017