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%I #16 Mar 19 2017 13:56:14
%S 1,0,0,0,0,0,0,0,0,0,1,1,10,11,65,77,350,440,1700,2244,7752,10659,
%T 33915,48279,144210,211508,600875,904475,2466750,3798795,10015005,
%U 15737864,40320149,64512209,161280568,262255753,641885440,1059105390,2544612396
%N a(1) = 1; a(2) = 0; a(3) = 0; a(4) = 0; a(5) = 0; a(6) = 0; a(7) = 0; a(8) = 0; a(9) = 0; a(10) = 0; a(n) = a(n - 1) + 9a(n - 2) - 8a(n - 3) - 28a(n - 4) + 21a(n - 5) + 35a(n - 6) - 20a(n - 7) - 15a(n - 8) + 5a(n - 9) + a(n - 10) for n >= 11.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 9, -8, -28, 21, 35, -20, -15, 5, 1).
%F G.f.:((5*x^4-5*x^2+1)*(x^5-3*x^4-3*x^3+4*x^2+x-1))/((x-1)*(x^3-2*x^2-x+1)*(x^6+8*x^5+8*x^4-6*x^3-6*x^2+x+1)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]
%p a[1]:=1: a[2]:=0: a[3]:=0: a[4]:=0: a[5]:=0: a[6]:=0: a[7]:=0: a[8]:=0: a[9]:=0: a[10]:=0: for n from 11 to 39 do a[n]:=a[n-1]+9*a[n-2]-8*a[n-3]-28*a[n-4]+21*a[n-5]+35*a[n-6]-20*a[n-7]-15*a[n-8]+5*a[n-9]+a[n-10] od: seq(a[n],n=1..39);
%t M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 5, -15, -20, 35, 21, -28, -8, 9, 1}}; v[1] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}; v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
%t LinearRecurrence[{1,9,-8,-28,21,35,-20,-15,5,1},{1,0,0,0,0,0,0,0,0,0},50] (* _Harvey P. Dale_, Dec 03 2014 *)
%Y Cf. A066170.
%K nonn
%O 1,13
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 20 2006
%E Edited by _N. J. A. Sloane_, Oct 08 2006
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