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Number of nondecreasing arrangements of n numbers x(i) in -(2n-2)..(2n-2) with the sum of sign(x(i))*2^|x(i)| zero.
1

%I #14 Sep 18 2024 08:29:01

%S 0,2,7,30,144,597,2742,12148,54696,247482,1120330,5099759,23249035,

%T 106285418,486878283,2234333944,10271022863,47283130811,217962771486,

%U 1005958652638,4647869260260,21496269109425,99510938004788,461047642206301,2137763442289891,9919444208575431,46058149007746511,213991712768042425,994811217776431456,4627232005483362687

%N Number of nondecreasing arrangements of n numbers x(i) in -(2n-2)..(2n-2) with the sum of sign(x(i))*2^|x(i)| zero.

%e All solutions for n=3

%e .-1...-3...-4...-3...-1...-2...-2

%e .-1....2....3...-3....0....1...-2

%e ..2....2....3....4....0....1....3

%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 a[n_] := a[n] = AatE[n, n, 2 n - 2];

%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 30}] (* _Jean-François Alcover_, Sep 18 2024, after _R. J. Mathar_ in A187988 *)

%Y Main diagonal of A187988.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 18 2011

%E a(10)-a(30) from _Jean-François Alcover_, Sep 18 2024