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A084613 a(n) = sum of absolute values of coefficients of (1 + x - 2*x^2)^n.

%I A084613 #17 Mar 26 2023 03:50:34
%S A084613 1,4,14,44,124,394,1418,4706,14322,40712,135878,468934,1513650,
%T A084613 4502864,13421408,45258442,152708520,483810550,1413811358,4483843328,
%U A084613 15051967962,49724234652,154802614364,461020649750,1486736569982
%N A084613 a(n) = sum of absolute values of coefficients of (1 + x - 2*x^2)^n.
%H A084613 G. C. Greubel, <a href="/A084613/b084613.txt">Table of n, a(n) for n = 0..1000</a>
%t A084613 Table[Total[Abs[CoefficientList[Expand[(1+x-2x^2)^n],x]]],{n,0,30}]  (* _Harvey P. Dale_, Apr 21 2011 *)
%o A084613 (PARI) for(n=0,40,S=0; for(k=0,2*n,t=polcoeff((1+x-2*x^2)^n,k,x); S=S+abs(t)); print1(S","))
%o A084613 (Magma)
%o A084613 A084612:= func< n,k | (&+[Binomial(n, k-j)*Binomial(k-j, j)*(-2)^j: j in [0..k]]) >;
%o A084613 [(&+[Abs(A084612(n,k)): k in [0..2*n]]): n in [0..50]]; // _G. C. Greubel_, Mar 25 2023
%o A084613 (SageMath)
%o A084613 def A084612(n,k): return sum(binomial(n,k-j)*binomial(k-j,j)*(-2)^j for j in range(k+1))
%o A084613 def A084613(n): return sum(abs(A084612(n,k)) for k in range(2*n+1))
%o A084613 [A084613(n) for n in range(51)] # _G. C. Greubel_, Mar 25 2023
%Y A084613 Cf. A002426, A084600 to A084612, A084614, A084615.
%K A084613 nonn
%O A084613 0,2
%A A084613 _Paul D. Hanna_, Jun 01 2003