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%I #13 Mar 06 2023 09:27:00
%S 0,3,5,12,33,92,257,715,1988,5529,15377,42745,118775,330015,917059,
%T 2548644,7083187,19684909,54704928,152026360,422489498,1174129226,
%U 3262989670,9068054805,25200655379,70034119048,194629155239,540886699852,1503158050714,4177369402390,11609167438104,32262594620909
%N Expansion of x*(1-x)*(3-13*x+24*x^2-17*x^3-18*x^4+35*x^5-3*x^6-14*x^7+x^9) / (1-7*x+20*x^2-30*x^3+16*x^4+20*x^5-32*x^6+6*x^7+11*x^8-2*x^9-x^10).
%H Colin Barker, <a href="/A323270/b323270.txt">Table of n, a(n) for n = 0..1000</a>
%H K. A. Van'kov, V. M. Zhuravlyov, <a href="https://www.mccme.ru/free-books/matpros/pdf/mp-22.pdf#page=127">Regular tilings and generating functions</a>, Mat. Pros. Ser. 3, issue 22, 2018 (127-157) [in Russian]. See Theorem 3.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (7,-20,30,-16,-20,32,-6,-11,2,1).
%F a(n) = 7*a(n-1) - 20*a(n-2) + 30*a(n-3) - 16*a(n-4) - 20*a(n-5) + 32*a(n-6) - 6*a(n-7) - 11*a(n-8) + 2*a(n-9) + a(n-10). - _Colin Barker_, Jan 10 2019
%t CoefficientList[Series[x(1-x)(3-13x+24x^2-17x^3-18x^4+35x^5- 3x^6- 14x^7+ x^9) / (1-7x+20x^2-30x^3+16x^4+20x^5-32x^6+ 6x^7+ 11x^8-2x^9-x^10),{x,0,50}],x] (* or *) LinearRecurrence[{7,-20,30,-16,-20,32,-6,-11,2,1},{0,3,5,12,33,92,257,715,1988,5529,15377,42745},40] (* _Harvey P. Dale_, Mar 06 2023 *)
%o (PARI) concat(0, Vec(x*(1 - x)*(3 - 13*x + 24*x^2 - 17*x^3 - 18*x^4 + 35*x^5 - 3*x^6 - 14*x^7 + x^9) / (1 - 7*x + 20*x^2 - 30*x^3 + 16*x^4 + 20*x^5 - 32*x^6 + 6*x^7 + 11*x^8 - 2*x^9 - x^10) + O(x^40))) \\ _Colin Barker_, Jan 10 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jan 09 2019
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