A241351 Number of n X 3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

4, 9, 19, 55, 72, 124, 243, 370, 695, 956, 1417, 2469, 3404, 5728, 8713, 12387, 19273, 29598, 44909, 73642, 107481, 163546, 255220, 378761, 599088, 925233, 1374249, 2146719, 3251091, 4948266, 7795540, 11712323, 17982730, 27767716, 41826534

Offset

1,1

Comments

Column 3 of A241356.

Links

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

Formula

Empirical: a(n) = 3*a(n-5) +4*a(n-6) +5*a(n-8) +2*a(n-9) +16*a(n-11) +3*a(n-13) +6*a(n-14) -10*a(n-15) -22*a(n-16) -2*a(n-17) -13*a(n-18) +26*a(n-19) -18*a(n-20) +18*a(n-21) -49*a(n-22) -2*a(n-23) -21*a(n-24) +18*a(n-25) +22*a(n-26) +61*a(n-27) -62*a(n-28) -13*a(n-29) -102*a(n-30) -32*a(n-31) +71*a(n-32) +43*a(n-33) +30*a(n-34) +53*a(n-35) -34*a(n-36) -204*a(n-37) +137*a(n-38) -22*a(n-39) +80*a(n-40) +108*a(n-41) +118*a(n-42) -242*a(n-43) +150*a(n-44) -100*a(n-45) +49*a(n-46) -3*a(n-47) +176*a(n-48) -162*a(n-49) +87*a(n-50) -118*a(n-51) +40*a(n-52) -89*a(n-53) +74*a(n-54) -11*a(n-55) +4*a(n-56) -65*a(n-57) +62*a(n-58) -91*a(n-59) +20*a(n-60) -22*a(n-61) +38*a(n-62) -20*a(n-63) +21*a(n-64) -19*a(n-65) +7*a(n-66) -5*a(n-67) +2*a(n-68) for n>85.

Example

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

Crossrefs

Cf. A241356.

Sequence in context: A326340 A183304 A359278 * A023377 A187408 A211055

Adjacent sequences: A241348 A241349 A241350 * A241352 A241353 A241354

Keyword

nonn

Author

R. H. Hardin, Apr 20 2014

Status

approved