A133896 - OEIS

%I #8 Nov 12 2017 09:33:39

%S 3,4,5,6,7,12,13,14,15,21,22,23,26,30,31,34,35,39,42,43,44,50,51,52,

%T 53,58,59,60,61,62,66,67,68,69,70,71,75,76,77,78,79,84,85,86,87,93,94,

%U 95,98,102,103,106,107,111,114,115,116,122,123,124,125,130,131,132,133,134

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

%C 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.

%F 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)).

%F 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).

%t Select[Range[140], Mod[Binomial[# + 6, #], 6] == 0&] (* _Jean-François Alcover_, Nov 12 2017 *)

%o (PARI) isok(n) = !(binomial(n+6, n) % 6); \\ _Michel Marcus_, Nov 12 2017

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

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

%K nonn

%O 0,1

%A _Hieronymus Fischer_, Oct 20 2007