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%I #23 Sep 14 2017 04:13:56
%S 0,1,13,50,148,393,993,2450,5976,14497,35077,84770,204748,494409,
%T 1193721,2882018,6957936,16798081,40554301,97906898,236368324,
%U 570643785,1377656145,3325956338,8029569096,19385094817
%N a(n) = 3*a(n-1) - a(n-2) - a(n-3) + 12.
%H G. C. Greubel, <a href="/A121991/b121991.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4, 0, 1).
%F a(n) = ((11 - 7*sqrt(2))*(1 - sqrt(2))^n + (1 + sqrt(2))^n*(11 + 7*sqrt(2)) - 24*n - 22)/4 .
%F O.g.f.: -x(1+9x+2x^2)/((1-x)^2*(x^2+2x-1)) . - _R. J. Mathar_, Aug 22 2008
%F a(n) = -6(n+1)+(1+11*A000129(n+1)+3*A000129(n))/2. - _R. J. Mathar_, Aug 22 2008
%F E.g.f.: (1/2)*(11*cosh(sqrt(2)*x) + 7*sqrt(2)*sinh(sqrt(2)*x) - (12*x + 11))*exp(x). - _G. C. Greubel_, Sep 14 2017
%t RecurrenceTable[{a[n] == 3*a[n - 1] - a[n - 2] - a[n - 3] + 12, a[0] == 0, a[1] == 1, a[2] == 13}, a, {n,0,50}] (* or *) LinearRecurrence[{4,-4,0,1}, {0,1,13,50}, 50] (* _G. C. Greubel_, Sep 14 2017 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(-x(1+9x+2x^2)/((1-x)^2*(x^2+2x-1))) ) \\ _G. C. Greubel_, Sep 14 2017
%Y Cf. A003215, A005891.
%K nonn,easy
%O 0,3
%A _Roger L. Bagula_, Sep 10 2006
%E Edited by _N. J. A. Sloane_, Aug 24 2008, Dec 30 2008
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