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%I #16 Mar 07 2024 16:35:12
%S 0,0,4,14,36,116,378,1178,3700,11694,36852,116082,365886,1153178,
%T 3634154,11453184,36095524,113756584,358508862,1129858168,3560801564,
%U 11222032838,35366766278,111460034016,351271552234,1107048863804,3488916716866,10995485596894
%N The sequence d[n] defined in A126939.
%C Linear recurrence and empirical g.f confirmed for more terms. - _Ray Chandler_, Mar 07 2024
%H Ray Chandler, <a href="/A126943/b126943.txt">Table of n, a(n) for n = 0..2006</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, 7, 3, 3, 1).
%F Empirical g.f.: -2*x^2*(x+1)*(x^2+x+2) / (x^6+3*x^5+3*x^4+7*x^3+x^2+2*x-1). - _Colin Barker_, Apr 08 2013
%t a[0] = 0; a[1] = 0; a[2] = 4; a[3] = 14; a[4] = 36; a[5] = 116; a[n_] := a[n] = a[n-6] + 3*a[n-5] + 3*a[n-4] + 7*a[n-3] + a[n-2] + 2*a[n-1]; Table[a[n], {n, 0, 27}] (* _Jean-François Alcover_, Nov 23 2016 *)
%t LinearRecurrence[{2, 1, 7, 3, 3, 1}, {0, 0, 4, 14, 36, 116}, 28] (* or *)
%t CoefficientList[ Series[-2x^2*(x + 1)*(x^2 + x + 2)/(x^6 + 3x^5 + 3x^4 + 7x^3 + x^2 + 2x - 1), {x, 0, 27}], x] (* _Robert G. Wilson v_, Nov 23 2016 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Mar 18 2007
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