A200041 Number of -n..n arrays x(0..4) of 5 elements with sum zero and with zeroth through 4th differences all nonzero

0, 26, 264, 1074, 3054, 7104, 14156, 25546, 42928, 67782, 102250, 148624, 209216, 286370, 383924, 503834, 650334, 826512, 1036716, 1283846, 1574252, 1909734, 2297538, 2740864, 3246472, 3817174, 4462780, 5184398, 5992386, 6889492, 7886048

Offset

1,2

Comments

Row 5 of A200038

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = -a(n-1) -2*a(n-2) -2*a(n-3) -2*a(n-4) -a(n-5) +a(n-7) +2*a(n-8) +3*a(n-9) +3*a(n-10) +4*a(n-11) +4*a(n-12) +4*a(n-13) +4*a(n-14) +3*a(n-15) +3*a(n-16) +a(n-17) +a(n-18) -a(n-19) -2*a(n-20) -4*a(n-21) -5*a(n-22) -7*a(n-23) -7*a(n-24) -8*a(n-25) -7*a(n-26) -7*a(n-27) -5*a(n-28) -4*a(n-29) -2*a(n-30) +2*a(n-32) +4*a(n-33) +5*a(n-34) +7*a(n-35) +7*a(n-36) +8*a(n-37) +7*a(n-38) +7*a(n-39) +5*a(n-40) +4*a(n-41) +2*a(n-42) +a(n-43) -a(n-44) -a(n-45) -3*a(n-46) -3*a(n-47) -4*a(n-48) -4*a(n-49) -4*a(n-50) -4*a(n-51) -3*a(n-52) -3*a(n-53) -2*a(n-54) -a(n-55) +a(n-57) +2*a(n-58) +2*a(n-59) +2*a(n-60) +a(n-61) +a(n-62)

Example

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

Crossrefs

Sequence in context: A251673 A059744 A016106 * A092723 A187695 A328874

Adjacent sequences: A200038 A200039 A200040 * A200042 A200043 A200044

Keyword

nonn

Author

R. H. Hardin Nov 12 2011

Status

approved