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 A074193 #26 Dec 04 2020 21:11:57
%S A074193 6,-1,-3,-1,17,-16,-15,13,81,-127,-58,175,329,-885,-31,1424,833,-5543,
%T A074193 2181,9233,-2298,-31025,27893,49495,-54879,-150416,245697,204965,
%U A074193 -526887,-570895,1801670,407711,-3882303,-946397,11542929,-3442672,-24121039,10317745,64959629,-56727711,-127083514
%N A074193 Sum of determinants of 2nd order principal minors of powers of the matrix ((1,1,0,0),(1,0,1,0),(1,0,0,1),(1,0,0,0)).
%C A074193 From _Kai Wang_, Oct 21 2020: (Start)
%C A074193 Let f(x) = x^4 - x^3 - x^2 - x - 1 be the characteristic polynomial for Tetranacci numbers (A000078). Let {x1,x2,x3,x4} be the roots of f(x). Then a(n) = (x1*x2)^n + (x1*x3)^n + (x1*x4)^n + (x2*x3)^n + (x2*x4)^n + (x3*x4)^n.
%C A074193 Let g(y) = y^6 + y^5 + 2*y^4 + 2*y^3 - 2*y^2 + y - 1 be the characteristic polynomial for a(n). Let {y1,y2,y3,y4,y5,y6} be the roots of g(y). Then a(n) = y1^n + y2^n + y3^n + y4^n + y5^n + y6^n. (End)
%H A074193 Michael De Vlieger, <a href="/A074193/b074193.txt">Table of n, a(n) for n = 0..5052</a>
%H A074193 Kai Wang, <a href="https://doi.org/10.13140/RG.2.2.19649.79209">Identities, generating functions and Binet formula for generalized k-nacci sequences</a>, 2020.
%H A074193 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-2,-2,2,-1,1).
%F A074193 a(n) = -a(n-1)-2a(n-2)-2a(n-3)+2a(n-4)-a(n-5)+a(n-6).
%F A074193 G.f.: (6+5x+8x^2+6x^3-4x^4+x^5)/(1+x+2x^2+2x^3-2x^4+x^5-x^6).
%F A074193 abs(a(n)) = abs(A074453(n)). - _Joerg Arndt_, Oct 22 2020
%t A074193 CoefficientList[Series[(6+5*x+8*x^2+6*x^3-4*x^4+x^5)/(1+x+2*x^2+2*x^3-2*x^4+x^5-x^6), {x, 0, 50}], x]
%o A074193 (PARI) polsym(x^6 + x^5 + 2*x^4 + 2*x^3 - 2*x^2 + x - 1,44) \\ _Joerg Arndt_, Oct 22 2020
%Y A074193 Cf. A073817, A073937, A000078, A074081.
%K A074193 easy,sign
%O A074193 0,1
%A A074193 Mario Catalani (mario.catalani(AT)unito.it), Aug 20 2002