A289133 a(n) is the number of odd integers divisible by 9 in ]2*(n-1)^2, 2*n^2[.

0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18

Offset

0,9

Comments

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

Links

Table of n, a(n) for n=0..80.

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

Formula

a(n + 9*k) = a(n) + 2*k.

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

Mathematica

Table[Count[Mod[Table[2((n-1)^2 +k)-1, {k, 1, 2 n-1}], 9], 0], {n, 0, 50}]

Prog

(PARI) a(n) = sum(k=2*(n-1)^2, 2*n^2, ((k % 2) && ((k % 9) == 0))); \\ Michel Marcus, Jun 26 2017

Crossrefs

Cf. A289120, A289122, A288156, A004523, A289139.

Sequence in context: A097882 A108955 A108956 * A367194 A135297 A176146

Adjacent sequences: A289130 A289131 A289132 * A289134 A289135 A289136

Keyword

nonn,easy

Author

Ralf Steiner, Jun 25 2017

Extensions

More terms from Michel Marcus, Jun 26 2017

Status

approved