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 A134160 #15 Jul 20 2024 17:47:07
%S A134160 163,7411,49981,180793,477463,1042303,2002321,3509221,5739403,8893963,
%T A134160 13198693,18904081,26285311,35642263,47299513,61606333,78936691,
%U A134160 99689251,124287373,153179113,186837223,225759151,270467041,321507733
%N A134160 a(n) = 163 + 1053*n + 2520*n^2 + 2646*n^3 + 1029*n^4.
%C A134160 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 A134160 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A134160 a(n) = (3*(7*n + 4)^4 + 6*(7*n + 4)^3 - 3*(7*n + 4) + 1)/7.
%F A134160 a(n) = sum(k=1..7*n+4, k^6) / sum(k=1..7*n+4, k^2).
%F A134160 G.f.: (163+6596*x+14556*x^2+3368*x^3+13*x^4)/(1-x)^5. - _Colin Barker_, May 25 2012
%t A134160 Table[(3(7n + 4)^4 + 6(7n + 4)^3 - 3 (7n + 4) + 1)/7, {n, 0, 100}] (*Artur Jasinski*)
%t A134160 Table[Sum[k^6, {k, 1, 7n + 4}]/Sum[k^2, {k, 1, 7n + 4}], {n, 0, 100}] (*Artur Jasinski*)
%t A134160 LinearRecurrence[{5,-10,10,-5,1},{163,7411,49981,180793,477463},30] (* _Harvey P. Dale_, Jul 20 2024 *)
%o A134160 (PARI) a(n)=163+1053*n+2520*n^2+2646*n^3+1029*n^4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A134160 Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134159, A134161.
%K A134160 nonn,easy
%O A134160 0,1
%A A134160 _Artur Jasinski_, Oct 10 2007