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%I #13 Aug 12 2024 09:11:13
%S 1,0,3,4,20,26,101,168,445,813,1804,3246,6527,11455,21193,36168,63077,
%T 104034,173255,277043,443629,689569,1068616,1618029,2438122,3605596,
%U 5300598,7674008,11039330,15676558,22120111,30867691,42805706,58792192,80263432,108650796
%N Poincaré series [or Poincare series] P(C#_{4,2}; x).
%H Dragomir Z. Djokovic, <a href="http://arXiv.org/abs/math.AC/0609262">Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices</a>. See Table 7.
%H <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (0, 3, 4, 1, -10, -16, -10, 13, 42, 42, 8, -53, -94, -78, 2, 108, 160, 118, -14, -151, -216, -151, 10, 165, 236, 165, 10, -151, -216, -151, -14, 118, 160, 108, 2, -78, -94, -53, 8, 42, 42, 13, -10, -16, -10, 1, 4, 3, 0, -1).
%F G.f. = (1+10*x^4+12*x^5+38*x^6+93*x^8+131*x^9+235*x^10+299*x^11+473*x^12+560*x^13+714*x^14+761*x^15+876*x^16+830*x^17+876*x^18+761*x^19+714*x^20+560*x^21+473*x^22+299*x^23+235*x^24+131*x^25+93*x^26+46*x^27+38*x^28+12*x^29+10*x^30+x^34+46*x^7)/((1-x^2)^3*(1-x^3)^4*(1-x^4)^4*(1-x^5)^2*(1-x^6)).
%t CoefficientList[Series[(1+10x^4+12x^5+38x^6+93x^8+131x^9+235x^10+299x^11+473x^12+560x^13+714x^14+761x^15+876x^16+830x^17+876x^18+761x^19+714x^20+560x^21+473x^22+299x^23+235x^24+131x^25+93x^26+46x^27+38x^28+12x^29+10x^30+x^34+46x^7)/((1-x^2)^3(1-x^3)^4(1-x^4)^4(1-x^5)^2(1-x^6)),{x,0,40}],x] (* or *) LinearRecurrence[ {0,3,4,1,-10,-16,-10,13,42,42,8,-53,-94,-78,2,108,160,118,-14,-151,-216,-151,10,165,236,165,10,-151,-216,-151,-14,118,160,108,2,-78,-94,-53,8,42,42,13,-10,-16,-10,1,4,3,0,-1},{1,0,3,4,20,26,101,168,445,813,1804,3246,6527,11455,21193,36168,63077,104034,173255,277043,443629,689569,1068616,1618029,2438122,3605596,5300598,7674008,11039330,15676558,22120111,30867691,42805706,58792192,80263432,108650796,146238779,195349646,259543886,342507386,449688513,586807417,762073528,984190432,1265332030,1618520444,2061547569,2613576998,3300278494,4149432584},40] (* _Harvey P. Dale_, Aug 11 2024 *)
%K nonn,changed
%O 0,3
%A _N. J. A. Sloane_, Dec 21 2006
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