A187980 Number of nondecreasing arrangements of n numbers x(i) in -(n-1)..(n-1) with the sum of sign(x(i))*2^|x(i)| zero.

0, 1, 3, 9, 36, 117, 411, 1452, 5040, 17829, 62870, 222458, 789895, 2808018, 10006020, 35713288, 127657287, 456975112, 1637845137, 5876993799, 21110257429, 75900966585, 273140226328, 983733709424, 3545658087397, 12788512426396, 46155740640489, 166684398100813, 602296651467057, 2177492178467267, 7876245417001355

Offset: 1

Author

R. H. Hardin, Mar 18 2011

Keywords

• nonn

Examples

			All solutions for n=3:
.-1...-2...-1
.-1....1....0
..2....1....0
		

Crossrefs

Column 1 of A187988.

Programs

Mathematica

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[n_, k_] := AatE[n, n, n + k - 2];
Table[T[n, 1], {n, 1, 31}] (* Jean-François Alcover, Sep 18 2024, after R. J. Mathar in A187988 *)

Extensions

More terms from R. J. Mathar, May 11 2023