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 A120711 #14 Feb 16 2025 08:33:01
%S A120711 0,14,32,150,492,1894,6724,24854,89972,329238,1197972,4372054,
%T A120711 15930580,58096214,211770452,772129110,2814859092,10262536534,
%U A120711 37414140244,136403674454,497291840852,1813006427478,6609762501972,24097566365014
%N A120711 Expansion of 2*x*(7+16*x-2*x^2-14*x^3)/(1-11*x^2-12*x^3+10*x^4+12*x^5).
%C A120711 Former title: 7 X 7 matrix Matrov of seven vertex Fano Plane: Characteristic polynomial: 12 + 10*x - 24*x^2 - 21*x^3 + 12*x^4 + 12*x^5 - x^7.
%H A120711 G. C. Greubel, <a href="/A120711/b120711.txt">Table of n, a(n) for n = 0..1000</a>
%H A120711 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FanoPlane.html">Fano Plane</a>
%H A120711 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,11,12,-10,-12).
%F A120711 a(n) = 11*a(n-2) + 12*a(n-3) - 10*a(n-4) - 12*a(n-5).
%F A120711 G.f.: 2*x*(7+16*x-2*x^2-14*x^3)/((1-x)*(1+x)*(1+2*x)*(1-2*x-6*x^2)). - _Colin Barker_, Mar 26 2012
%F A120711 a(n) = (1/3)*(-1 - 3*(-1)^n + (-2)^(n+1) + 6*(A083099(n+1) + 4*A083099(n))). - _G. C. Greubel_, Jul 22 2023
%t A120711 M = {{0,1,0,0,0,1,1}, {1,0,1,0,0,0,1}, {0,1,0,1,0,0,1}, {0,0,1,0,1,0, 1}, {0,0,0,1,0,1,1}, {1,0,0,0,1,0,1}, {1,1,1,1,1,1,0}};
%t A120711 v[1] = {0,1,1,2,3,5,8}; v[n_]:= v[n]= M.v[n-1];
%t A120711 Table[v[n][[1]], {n,50}]
%t A120711 LinearRecurrence[{0,11,12,-10,-12}, {0,14,32,150,492}, 40] (* _G. C. Greubel_, Jul 22 2023 *)
%o A120711 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( 2*x*(7+16*x-2*x^2-14*x^3)/(1-11*x^2-12*x^3+10*x^4+12*x^5) )); // _G. C. Greubel_, Jul 22 2023
%o A120711 (SageMath)
%o A120711 A083099=BinaryRecurrenceSequence(2,6,0,1)
%o A120711 def A120711(n): return (1/3)*(-1 -3*(-1)^n +(-2)^(n+1) +6*(A083099(n+1) +4*A083099(n)))
%o A120711 [A120711(n) for n in range(41)] # _G. C. Greubel_, Jul 22 2023
%Y A120711 Cf. A083099, A111384.
%K A120711 nonn,easy
%O A120711 0,2
%A A120711 _Roger L. Bagula_, Aug 12 2006
%E A120711 Edited by _G. C. Greubel_, Jul 22 2023