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 A267167 #29 Oct 18 2022 14:53:29
%S A267167 1,5,14,31,59,101,161,243,351,488,658,865,1112,1403,1741,2130,2574,
%T A267167 3077,3643,4274,4974,5747,6597,7528,8543,9646,10840,12129,13517,15007,
%U A267167 16603,18309,20129,22066,24123,26304,28613,31054,33631,36347,39205,42209,45363,48671,52136,55762,59553,63512,67643,71949,76434,81102,85957,91003,96242
%N A267167 Growth series for affine Coxeter group B_4.
%D A267167 N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10b, page 231, W_a(t).
%H A267167 G. C. Greubel, <a href="/A267167/b267167.txt">Table of n, a(n) for n = 0..10000</a>
%H A267167 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,2,-2,1,0,0,-1,2,-1).
%F A267167 The growth series for the affine Coxeter group of type B_k (k >= 2) has g.f. = Product_i (1-x^{m_i+1})/((1-x)*(1-x^{m_i})) where the m_i are [1,3,5,...,2k-1].
%F A267167 Here (k=4) the G.f. is (1+t+t^2+t^3+t^4+t^5+t^6+t^7)*(t^3+1)*(1+t+t^2+t^3)*(1+t) / (-1+t^7)/(-1+t^5)/(-1+t)^2.
%F A267167 a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + a(n-9) - a(n-12) + 2*a(n-13) - a(n-14), n > 0. - _Muniru A Asiru_, Oct 25 2018
%p A267167 seq(coeff(series((1-x^2)*(1+x^3)*(1-x^4)*(1-x^8)/((1-x)^5*(1-x^5)*(1-x^7)),x,n+1), x, n), n = 0 .. 55); # _Muniru A Asiru_, Oct 25 2018
%t A267167 CoefficientList[Series[(1-t^2)*(1+t^3)*(1-t^4)*(1-t^8)/((1-t)^5*(1-t^5)*(1 - t^7)), {t, 0, 50}], t] (* _G. C. Greubel_, Oct 24 2018 *)
%o A267167 (PARI) t='t+O('t^40); Vec((1-t^2)*(1+t^3)*(1-t^4)*(1-t^8)/((1-t)^5*(1-t^5)*(1 - t^7))) \\ _G. C. Greubel_, Oct 24 2018
%o A267167 (Magma) m:=40; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-t^2)*(1+t^3)*(1-t^4)*(1-t^8)/((1-t)^5*(1-t^5)*(1 - t^7)))); // _G. C. Greubel_, Oct 24 2018
%Y A267167 The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696-A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167-A267175.
%K A267167 nonn,easy
%O A267167 0,2
%A A267167 _N. J. A. Sloane_, Jan 11 2016