A133899 Numbers m such that binomial(m+9,m) mod 9 = 0.

72, 73, 74, 75, 76, 77, 78, 79, 80, 153, 154, 155, 156, 157, 158, 159, 160, 161, 234, 235, 236, 237, 238, 239, 240, 241, 242, 315, 316, 317, 318, 319, 320, 321, 322, 323, 396, 397, 398, 399, 400, 401, 402, 403, 404, 477, 478, 479, 480, 481, 482, 483, 484, 485

Offset: 0

Author

Hieronymus Fischer, Oct 20 2007

Keywords

• nonn

Comments

Also numbers m such that floor(1+(m/9)) mod 9 = 0.

Partial sums of the sequence 72,1,1,1,1,1,1,1,1,73,1,1,1,1,1,1,1,1,73, ... which has period 9.

Crossrefs

Cf. A000040, A133620, A133621, A133623, A133630, A133635.

Cf. A133879, A133889, A133890, A133900, A133910.

Programs

Mathematica

Select[Range[500],Divisible[Binomial[#+9,#],9]&] (* Harvey P. Dale, Apr 03 2011 *)

Formula

a(n)=9n+72-8*(n mod 9).

G.f.: g(x)=(72+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9)/((1-x^9)(1-x)).

G.f.: g(x)=(72-71x-x^10) /((1-x^9)(1-x)^2).