A187988 T(n,k)=Number of nondecreasing arrangements of n numbers x(i) in -(n+k-2)..(n+k-2) with the sum of sign(x(i))*2^|x(i)| zero

0, 0, 1, 0, 2, 3, 0, 3, 5, 9, 0, 4, 7, 15, 36, 0, 5, 9, 22, 57, 117, 0, 6, 11, 30, 82, 181, 411, 0, 7, 13, 39, 111, 260, 632, 1452, 0, 8, 15, 49, 144, 355, 912, 2199, 5040, 0, 9, 17, 60, 181, 467, 1257, 3158, 7593, 17829, 0, 10, 19, 72, 222, 597, 1673, 4357, 10920, 26706, 62870

Offset

1,5

Comments

Table starts

.....0.....0.....0.....0.....0.....0.....0.....0....0....0...0...0..0..0.0

.....1.....2.....3.....4.....5.....6.....7.....8....9...10..11..12.13.14

.....3.....5.....7.....9....11....13....15....17...19...21..23..25.27

.....9....15....22....30....39....49....60....72...85...99.114.130

....36....57....82...111...144...181...222...267..316..369.426

...117...181...260...355...467...597...746...915.1105.1317

...411...632...912..1257..1673..2166..2742..3407.4167

..1452..2199..3158..4357..5825..7592..9689.12148

..5040..7593.10920.15146.20404.26835.34588

.17829.26706.38385.53379.72246.95590

Links

R. J. Mathar, Table of n, a(n) for n = 1..187 augmenting an earlier file with 117 entries by R. H. Hardin .

R. J. Mathar, Background on the recurrent Maple program for the linear diophantine equation

Example

Some solutions for n=5 k=3
.-3...-6...-5...-3...-3...-6...-4...-4...-1...-4...-2...-4...-4...-2...-3...-5
.-3...-3...-5...-1...-3...-5...-1...-2...-1...-4...-2...-2...-4...-1....1...-1
.-2...-3...-2....1...-3...-5....0...-2....0...-4...-1....2...-3....1....1....1
..2....4....2....2...-3....6....0....3....0...-4....1....3....3....1....1....4
..4....6....6....2....5....6....4....4....1....6....3....3....5....1....1....4

Maple

AatE := proc(n, nminusfE, E)
    option remember ;
    local a, fEminus, fEplus, f0, resn ;
    if E = 0 then
        if n =0 then
            1;
        else
            0;
        end if;
    else
        a :=0 ;
        for fEminus from 0 to nminusfE do
            for fEplus from 0 to nminusfE-fEminus do
                f0 := nminusfE-fEminus-fEplus ;
                resn := n-(2^E+1)*fEminus+(2^E-1)*fEplus ;
                if abs (resn) <= (1+2^(E-1))*f0 then
                    a := a+procname(resn, f0, E-1) ;
                end if;
            end do:
        end do:
        a ;
    end if;
end proc:
A187988 := proc(n, k)
    AatE(n, n, n+k-2) ;
end proc:
seq(seq( A187988(n, d-n), n=1..d-1), d=2..15) ; # R. J. Mathar, May 12 2023

Crossrefs

Row n=4 is A055999(k+1). A187989 (n=5), A187990 (n=6), A187991 (n=7), A187992 (n=8), A187979 (k=n), A187980 (k=1), A187981 (k=2), A187982 (k=3), A187983 (k=4), A187984 (k=5), A187985 (k=6).

Sequence in context: A047773 A279416 A331781 * A035549 A329970 A245255

Adjacent sequences: A187985 A187986 A187987 * A187989 A187990 A187991

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2011

Status

approved