A133896 Numbers m such that binomial(m+6,m) mod 6 = 0.

3, 4, 5, 6, 7, 12, 13, 14, 15, 21, 22, 23, 26, 30, 31, 34, 35, 39, 42, 43, 44, 50, 51, 52, 53, 58, 59, 60, 61, 62, 66, 67, 68, 69, 70, 71, 75, 76, 77, 78, 79, 84, 85, 86, 87, 93, 94, 95, 98, 102, 103, 106, 107, 111, 114, 115, 116, 122, 123, 124, 125, 130, 131, 132, 133, 134

Offset: 0

Author

Hieronymus Fischer, Oct 20 2007

Keywords

• nonn

Comments

Partial sums of the sequence 3,1,1,1,1,5,1,1,1,6,1,1,3,4,1,3,1,4,3,1,1,6,1,1,1,5,1,1,1,1,4,1,1,1,1,1,4, ... which has period 36.

Crossrefs

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

Cf. A133876, A133886, A133890, A133900, A133910.

Programs

Mathematica

Select[Range[140], Mod[Binomial[# + 6, #], 6] == 0&] (* Jean-François Alcover, Nov 12 2017 *)

PARI

isok(n) = !(binomial(n+6, n) % 6); \\ Michel Marcus, Nov 12 2017

Formula

G.f.: g(x)=3/(1-x)+ x/(1-x)^2+(4x^5+5x^9+2x^12+3x^13+2x^15+3x^17+2x^18+5x^21+3x^26+3x^32) /((1-x^36)(1-x)).

G.f.: g(x)=(3-2x+4x^5+5x^9+2x^12+3x^13+2x^15+3x^17+2x^18+5x^21+3x^26+3x^32-x^37) /((1-x^36)(1-x)^2).