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T(n+3,3) with T as in A036355.
1

%I #12 Jul 03 2022 08:05:24

%S 3,10,32,84,207,478,1060,2272,4744,9692,19446,38420,74909,144378,

%T 275464,520864,977005,1819426,3366182,6191056,11325040,20613800,

%U 37350060,67389320,121113335,216877274,387048080,688559356,1221323947

%N T(n+3,3) with T as in A036355.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4, -2, -8, 5, 8, -2, -4, -1).

%F G.f.: (-2x^2-2x+3)/(1-x-x^2)^4.

%F a(0)=3, a(1)=10, a(2)=32, a(3)=84, a(4)=207, a(5)=478, a(6)=1060, a(7)=2272, a(n)=4*a(n-1)-2*a(n-2)-8*a(n-3)+5*a(n-4)+8*a(n-5)- 2*a(n-6)- 4*a(n-7)-a(n-8) [From Harvey P. Dale, May 06 2012]

%F a(n) = 3*A001872(n)-2*A001872(n-1)-2*A001872(n-2) = A001872(n)+2*A001628(n). - _R. J. Mathar_, Jul 03 2022

%t CoefficientList[Series[(-2x^2-2x+3)/(1-x-x^2)^4,{x,0,30}],x] (* or *) LinearRecurrence[{4,-2,-8,5,8,-2,-4,-1},{3,10,32,84,207,478,1060,2272},30] (* _Harvey P. Dale_, May 06 2012 *)

%K nonn,easy

%O 0,1

%A _Floor van Lamoen_