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 A134161 #20 Sep 25 2024 04:11:53
%S A134161 373,10363,61723,210901,539041,1151983,2180263,3779113,6128461,
%T A134161 9432931,13921843,19849213,27493753,37158871,49172671,63887953,
%U A134161 81682213,102957643,128141131,157684261,192063313,231779263,277357783,329349241
%N A134161 a(n) = 373 + 1947*n + 3780*n^2 + 3234*n^3 + 1029*n^4.
%C A134161 A000540(n) is divisible by A000330(n) if and only n is congruent to {1,2,4,5} mod 7 (see A047380) A134158 is case when n is congruent to 1 mod 7 A134159 is case when n is congruent to 2 mod 7 A134160 is case when n is congruent to 4 mod 7 A134161 is case when n is congruent to 5 mod 7 A133180 is union of A134158 and A134159 and A134160 and A134161.
%H A134161 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A134161 a(n) = (3*(7*n + 5)^4 + 6*(7*n + 5)^3 - 3*(7*n + 5) + 1)/7.
%F A134161 a(n) = (Sum_{k=1..7*n+5} k^6) / (Sum_{k=1..7*n+5} k^2).
%F A134161 G.f.: -(373+8498*x+13638*x^2+2186*x^3+x^4)/(-1+x)^5. - _R. J. Mathar_, Nov 14 2007
%F A134161 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) with a(0)=373, a(1)=10363, a(2)=61723, a(3)=210901, and a(4)=539041. - _Harvey P. Dale_, Nov 25 2012
%t A134161 Table[(3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7, {n, 0, 100}]
%t A134161 Table[Sum[k^6, {k, 1, 7n + 5}]/Sum[k^2, {k, 1, 7n + 5}], {n, 0, 100}]
%t A134161 LinearRecurrence[{5,-10,10,-5,1},{373,10363,61723,210901,539041},100] (* _Harvey P. Dale_, Nov 25 2012 *)
%o A134161 (PARI) a(n)=373+1947*n+3780*n^2+3234*n^3+1029*n^4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A134161 Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134159, A134160.
%K A134161 nonn,easy
%O A134161 0,1
%A A134161 _Artur Jasinski_, Oct 10 2007