This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133897 #9 Mar 30 2025 14:19:17
%S A133897 42,43,44,45,46,47,48,91,92,93,94,95,96,97,140,141,142,143,144,145,
%T A133897 146,189,190,191,192,193,194,195,238,239,240,241,242,243,244,287,288,
%U A133897 289,290,291,292,293,336,337,338,339,340,341,342,385,386,387,388,389,390
%N A133897 Numbers m such that binomial(m+7,m) mod 7 = 0.
%C A133897 Also numbers m such that floor(1+(m/7)) mod 7 = 0.
%C A133897 Partial sums of the sequence 42,1,1,1,1,1,1,43,1,1,1,1,1,1,43,... which has period 7.
%H A133897 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A133897 a(n) = 7*n + 42 - 6*(n mod 7).
%F A133897 G.f.: (42+x+x^2+x^3+x^4+x^5+x^6+x^7)/((1-x^7)(1-x)).
%F A133897 G.f.: (42-41x-x^8) /((1-x^7)(1-x)^2).
%t A133897 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 *)
%Y A133897 Cf. A000040, A133620, A133621, A133623, A133630, A133635.
%Y A133897 Cf. A133877, A133887, A133890, A133900, A133910.
%K A133897 nonn,easy
%O A133897 0,1
%A A133897 _Hieronymus Fischer_, Oct 20 2007