%I #27 Sep 18 2024 08:17:34
%S 36,57,82,111,144,181,222,267,316,369,426,487,552,621,694,771,852,937,
%T 1026,1119,1216,1317,1422,1531,1644,1761,1882,2007,2136,2269,2406,
%U 2547,2692,2841,2994,3151,3312,3477,3646,3819,3996,4177,4362,4551,4744,4941
%N Number of nondecreasing arrangements of 5 numbers x(i) in -(n+3)..(n+3) with the sum of sign(x(i))*2^|x(i)| zero.
%H R. J. Mathar, <a href="/A187989/b187989.txt">Table of n, a(n) for n = 1..86</a> correcting the earlier _R. H. Hardin_ file at a(28).
%e Some solutions for n=3:
%e -6 -4 -4 -6 -4 -3 -4 -3 -6 -3 -3 -6 -4 -5 -5 -1
%e -1 -4 -4 -3 -1 -2 -3 0 -5 -3 -3 -1 1 -4 -2 -1
%e -1 -4 -3 3 1 -2 -3 0 5 -2 -3 1 1 3 -2 -1
%e 2 -4 3 5 3 3 4 1 5 2 -3 5 2 3 3 1
%e 6 6 5 5 3 3 4 2 5 4 5 5 3 5 5 2
%t AatE[n_, nminusfE_, E_] := AatE[n, nminusfE, E] = Module[{a, fEminus, fEplus, f0, resn}, If[E == 0, If[n == 0, 1, 0], a = 0; For[fEminus = 0, fEminus <= nminusfE, fEminus++, For[fEplus = 0, fEplus <= nminusfE - fEminus, fEplus++, f0 = nminusfE - fEminus - fEplus; resn = n - (2^E + 1)*fEminus + (2^E - 1)*fEplus; If[Abs[resn] <= (1 + 2^(E - 1))*f0, a = a + AatE[resn, f0, E - 1]]]]; a]];
%t T[n_, k_] := AatE[n, n, n + k - 2];
%t Table[T[5, k], {k, 1, 86}] (* _Jean-François Alcover_, Sep 18 2024, after _R. J. Mathar_ in A187988 *)
%Y Row 5 of A187988.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 18 2011
%E a(28) corrected by _R. J. Mathar_, May 09 2023