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Expansion of (1+2*x+4*x^2+4*x^3+6*x^4+4*x^5+x^6) / (1-3*x-x^2-6*x^3-7*x^4-7*x^5-5*x^6-x^7).
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%I #12 Mar 08 2023 12:43:16

%S 1,5,20,75,288,1105,4234,16226,62188,238340,913452,3500857,13417236,

%T 51422337,197079099,755317101,2894796675,11094476468,42520225774,

%U 162961236161,624558407329,2393656389397,9173827208656,35159225871899,134749776270503,516436347919005,1979272313718089

%N Expansion of (1+2*x+4*x^2+4*x^3+6*x^4+4*x^5+x^6) / (1-3*x-x^2-6*x^3-7*x^4-7*x^5-5*x^6-x^7).

%H Colin Barker, <a href="/A275908/b275908.txt">Table of n, a(n) for n = 0..1000</a>

%H T. Doslic, T. Short, <a href="http://arxiv.org/abs/1511.00590">Maximal matchings in polyspiro and benzenoid chains</a>, arXiv:1511.00590, [math.CO], 2015. See Th. 4.4.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,6,7,7,5,1).

%F a(n) = 3*a(n-1)+a(n-2)+6*a(n-3)+7*a(n-4)+7*a(n-5)+5*a(n-6)+a(n-7) for n>6. - _Colin Barker_, Aug 26 2016

%t CoefficientList[Series[(1+2x+4x^2+4x^3+6x^4+4x^5+x^6)/(1-3x-x^2-6x^3- 7x^4- 7x^5-5x^6-x^7),{x,0,30}],x] (* or *) LinearRecurrence[{3,1,6,7,7,5,1},{1,5,20,75,288,1105,4234},30] (* _Harvey P. Dale_, Mar 08 2023 *)

%o (PARI) Vec((1+2*x+4*x^2+4*x^3+6*x^4+4*x^5+x^6)/(1-3*x-x^2-6*x^3- 7*x^4-7*x^5-5*x^6-x^7) + O(x^30)) \\ _Colin Barker_, Aug 26 2016

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Aug 26 2016