A240757 Number of n X 3 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

11, 9, 19, 24, 25, 35, 45, 76, 117, 180, 265, 365, 533, 786, 1220, 1796, 2728, 4087, 6140, 9060, 13625, 20484, 30734, 46161, 69561, 104127, 156807, 235060, 353693, 530499, 798289, 1200045, 1804325, 2711062, 4074989, 6123683, 9207099, 13837742

Offset

1,1

Comments

Column 3 of A240760.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-5) +4*a(n-6) +a(n-7) +4*a(n-8) +5*a(n-9) -6*a(n-10) -12*a(n-11) -a(n-12) -13*a(n-13) -16*a(n-14) -7*a(n-15) +13*a(n-16) +2*a(n-17) +20*a(n-18) +24*a(n-19) +15*a(n-20) -3*a(n-21) -2*a(n-22) -20*a(n-23) -44*a(n-24) -11*a(n-25) +9*a(n-26) -82*a(n-27) -30*a(n-28) +19*a(n-29) -21*a(n-30) -108*a(n-31) +132*a(n-32) +43*a(n-33) -68*a(n-34) +17*a(n-35) +171*a(n-36) -171*a(n-37) +66*a(n-38) +206*a(n-39) -46*a(n-40) -124*a(n-41) +214*a(n-42) -29*a(n-43) -283*a(n-44) +123*a(n-45) +129*a(n-46) -251*a(n-47) -6*a(n-48) +164*a(n-49) -17*a(n-50) -121*a(n-51) +216*a(n-52) +51*a(n-53) -79*a(n-54) +40*a(n-55) +58*a(n-56) -21*a(n-57) -16*a(n-58) +32*a(n-59) -3*a(n-60) -47*a(n-61) -29*a(n-62) -9*a(n-63) -2*a(n-64) -11*a(n-65) -2*a(n-66) +10*a(n-67) -6*a(n-69) +12*a(n-70) +3*a(n-71) -4*a(n-72) -3*a(n-73) +3*a(n-74) +a(n-75) -3*a(n-76) for n>84.

Example

Some solutions for n=4
..2..2..2....2..2..2....2..2..2....3..1..3....2..1..1....3..1..3....2..2..2
..3..3..1....3..3..1....3..1..3....2..2..2....3..3..2....2..2..2....3..3..1
..2..0..2....2..2..2....2..0..2....3..1..2....2..1..2....2..1..3....2..2..2
..2..0..2....2..1..3....2..0..1....2..1..2....2..0..2....2..1..2....2..1..2

Crossrefs

Cf. A240760.

Sequence in context: A342162 A337227 A254716 * A206422 A316450 A196006

Adjacent sequences: A240754 A240755 A240756 * A240758 A240759 A240760

Keyword

nonn

Author

R. H. Hardin, Apr 12 2014

Status

approved