A289122 a(n) is number of odd integers divisible by 11 in the interval ]2*(n-1)^2, 2*n^2[.

0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 5, 5, 6, 5, 6, 6, 6, 6, 7, 6, 7, 7, 7, 8, 7, 8, 8, 8, 8, 9, 8, 9, 9, 9, 10, 9, 10, 10, 10, 10, 11, 10, 11, 11, 11, 12, 11, 12, 12, 12, 12, 13, 12, 13, 13, 13, 14, 13, 14, 14, 14, 14, 15

Offset: 0

Author

Ralf Steiner, Jun 25 2017

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A289120, A289133, A288156, A004523, A289139.

Programs

Mathematica

Table[Count[Mod[Table[2((n-1)^2 +k) -1,{k,1,2n-1}],11],0],{n,0,50}]
LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,1,-1},{0,0,0,1,0,1,1,1,2,1,2,2},90] (* Harvey P. Dale, Aug 24 2017 *)

PARI

a(n) = sum(k=2*(n-1)^2, 2*n^2, ((k % 2) && ((k % 11) == 0))); \\ Michel Marcus, Jun 26 2017

Formula

a(n + 11*k) = a(n) + 2*k. - David A. Corneth, Jun 25 2017

G.f.: (x^10-x^9+x^8+x^5-x^4+x^3)/(x^12-x^11-x+1). - Alois P. Heinz, Jun 26 2017