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 A167467 #25 Sep 08 2022 08:45:48
%S A167467 23,190,652,1559,3061,5308,8450,12637,18019,24746,32968,42835,54497,
%T A167467 68104,83806,101753,122095,144982,170564,198991,230413,264980,302842,
%U A167467 344149,389051,437698,490240,546827,607609,672736,742358,816625,895687,979694,1068796
%N A167467 a(n) = 25*n^3 - n*(5*n+1)/2 + 1.
%C A167467 Also the real part of f(x+n*f(x,y,z), y+n*f(x,y,z), z+n*f(x,y,z))/f(x,y,z) for f(x,y,z) = x^3+y^2+z at x=(-1+i*sqrt(3))/2, y=i and z=5.
%C A167467 If f(x,y,z) is a trivariate polynomial, f(x+n*f(x,y,z),y+n*f(x,y,z),z+n*f(x,y,z)) is congruent to 0 (mod f(x,y,z)).
%C A167467 The ratio f(x+n*f,y+n*f,z+n*f)/f of these two functions is decomposed into the real part (this sequence here), and the imaginary part. The imaginary part is 2*n*i + sqrt(3)*A167469(n)*i, where i=sqrt(-1) is the imaginary unit.
%H A167467 Harvey P. Dale, <a href="/A167467/b167467.txt">Table of n, a(n) for n = 1..1000</a>
%H A167467 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A167467 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A167467 G.f.: x*(23 + 98*x + 30*x^2 - x^3)/(1-x)^4.
%F A167467 E.g.f.: (2 + 44*x + 145*x^2 + 50*x^3)*exp(x)/2 -1. - _G. C. Greubel_, Apr 09 2016
%e A167467 f(x +f(x,y,z), y + f(x,y,z), z + f(x,y,z)) = (23 + 2i + 6*sqrt(3)*i)* f(x,y,z) at n=1.
%p A167467 f := proc(x,y,z) x^3+y^2+z ; end proc:
%p A167467 A167467 := proc(n) local rho,a ,x,y,z; a := f(x+n*f(x,y,z),y+n*f(x,y,z),z+n*f(x,y,z))/f(x,y,z) ; rho := (-1+I*sqrt(3))/2 ; a := subs({x = rho, y=I,z=5},a) ; a := expand(a) ; Re(a) ; end:
%p A167467 seq(A167467(n),n=1..50) ; # _R. J. Mathar_, Nov 12 2009
%t A167467 LinearRecurrence[{4,-6,4,-1},{23,190,652,1559},50] (* _Harvey P. Dale_, Sep 28 2012 *)
%o A167467 (PARI) a(n)=1+25*n^3-n*(5*n+1)/2 \\ _Charles R Greathouse IV_, Jul 07 2013
%o A167467 (Magma) [25*n^3 - n*(5*n+1)/2 + 1: n in [1..50]]; // _G. C. Greubel_, Sep 01 2019
%o A167467 (Sage) [25*n^3 - n*(5*n+1)/2 + 1 for n in (1..50)] # _G. C. Greubel_, Sep 01 2019
%o A167467 (GAP) List([1..50], n-> 25*n^3 - n*(5*n+1)/2 + 1); # _G. C. Greubel_, Sep 01 2019
%Y A167467 Cf. A165806, A165808, A165809, A166715, A166957, A167190.
%K A167467 nonn,easy
%O A167467 1,1
%A A167467 _A.K. Devaraj_, Nov 05 2009
%E A167467 a(2) and a(3) corrected, definition simplified and sequence extended by _R. J. Mathar_, Nov 12 2009