A133897 - OEIS

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

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OFFSET

0,1

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

Table of n, a(n) for n=0..54.

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

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).

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 *)

PROG

(Magma) [7*n + 42 - 6*(n mod 7) : n in [0..80]]; // Wesley Ivan Hurt, Feb 13 2026

CROSSREFS

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

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

Sequence in context: A221213 A165863 A008941 * A086848 A364219 A058904

Adjacent sequences: A133894 A133895 A133896 * A133898 A133899 A133900

KEYWORD

nonn,easy

AUTHOR

Hieronymus Fischer, Oct 20 2007

STATUS

approved