A187979 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.

0, 2, 7, 30, 144, 597, 2742, 12148, 54696, 247482, 1120330, 5099759, 23249035, 106285418, 486878283, 2234333944, 10271022863, 47283130811, 217962771486, 1005958652638, 4647869260260, 21496269109425, 99510938004788, 461047642206301, 2137763442289891, 9919444208575431, 46058149007746511, 213991712768042425, 994811217776431456, 4627232005483362687

Offset: 1

Author

R. H. Hardin, Mar 18 2011

Keywords

• nonn

Examples

			All solutions for n=3
.-1...-3...-4...-3...-1...-2...-2
.-1....2....3...-3....0....1...-2
..2....2....3....4....0....1....3
		

Crossrefs

Main diagonal 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]];
a[n_] := a[n] = AatE[n, n, 2 n - 2];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 30}] (* Jean-François Alcover, Sep 18 2024, after R. J. Mathar in A187988 *)

Extensions

a(10)-a(30) from Jean-François Alcover, Sep 18 2024