A133897 Numbers m such that binomial(m+7,m) mod 7 = 0.

42, 43, 44, 45, 46, 47, 48, 91, 92, 93, 94, 95, 96, 97, 140, 141, 142, 143, 144, 145, 146, 189, 190, 191, 192, 193, 194, 195, 238, 239, 240, 241, 242, 243, 244, 287, 288, 289, 290, 291, 292, 293, 336, 337, 338, 339, 340, 341, 342, 385, 386, 387, 388, 389, 390

Offset: 0

Author

Hieronymus Fischer, Oct 20 2007

Keywords

• nonn
• easy

Comments

Also numbers m such that floor(1+(m/7)) mod 7 = 0.

Partial sums of the sequence 42,1,1,1,1,1,1,43,1,1,1,1,1,1,43,... which has period 7.

Links

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

Crossrefs

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

Cf. A133877, A133887, A133890, A133900, A133910.

Programs

Mathematica

Select[Range[390],Mod[Binomial[#+7,#],7]==0&] (* or *) LinearRecurrence[{1,0,0,0,0,0,1,-1},{42, 43, 44, 45, 46, 47, 48, 91},55] (* James C. McMahon, Mar 30 2025 *)

Formula

a(n) = 7*n + 42 - 6*(n mod 7).

G.f.: (42+x+x^2+x^3+x^4+x^5+x^6+x^7)/((1-x^7)(1-x)).

G.f.: (42-41x-x^8) /((1-x^7)(1-x)^2).