A187979 - OEIS

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

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

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 *)

CROSSREFS

Main diagonal of A187988.

Sequence in context: A006013 A358965 A368933 * A358964 A366055 A368932

Adjacent sequences: A187976 A187977 A187978 * A187980 A187981 A187982

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 18 2011

EXTENSIONS

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

STATUS

approved