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A259001 Number of (n+2)X(3+2) 0..1 arrays with every 3X3 subblock sum of the two medians of the central row and column plus the two sums of the diagonal and antidiagonal nondecreasing horizontally, vertically and ne-to-sw antidiagonally. 1
9374, 18341, 55760, 116098, 142316, 191035, 134036, 138255, 135282, 125066, 136926, 137549, 144388, 157396, 164184, 173168, 185086, 194970, 199468, 222173, 221824, 227101, 257586, 254779, 269678, 292721, 283212, 305637, 337320, 325206 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 3 of A259006.
LINKS
FORMULA
Empirical: a(n) = -a(n-1) -a(n-2) +a(n-3) +a(n-4) +2*a(n-5) +a(n-6) +a(n-7) -a(n-8) -a(n-9) -a(n-10) +a(n-12) +a(n-13) +a(n-14) -a(n-15) -a(n-16) -2*a(n-17) -a(n-18) -a(n-19) +a(n-20) +a(n-21) +a(n-22) for n>36.
Also empirically a quasipolynomial of degree 2 with period 60, the first 12 being (empirical formulas for n>14):
for n mod 60 = 0: a(n) = (307/3)*n^2 + (175303/30)*n + 53785;
for n mod 60 = 1: a(n) = (3107/24)*n^2 + (109097/20)*n + (6308123/120);
for n mod 60 = 2: a(n) = (10769/72)*n^2 + (977923/180)*n + (2138171/45);
for n mod 60 = 3: a(n) = (307/3)*n^2 + (175303/30)*n + (523367/10);
for n mod 60 = 4: a(n) = (3107/24)*n^2 + (109097/20)*n + (815764/15);
for n mod 60 = 5: a(n) = (10769/72)*n^2 + (977923/180)*n + (3756257/72);
for n mod 60 = 6: a(n) = (307/3)*n^2 + (175303/30)*n + (289877/5);
for n mod 60 = 7: a(n) = (3107/24)*n^2 + (109097/20)*n + (5353751/120);
for n mod 60 = 8: a(n) = (10769/72)*n^2 + (977923/180)*n + (2363234/45);
for n mod 60 = 9: a(n) = (307/3)*n^2 + (175303/30)*n + (556181/10);
for n mod 60 = 10: a(n) = (3107/24)*n^2 + (109097/20)*n + (141317/3);
for n mod 60 = 11: a(n) = (10769/72)*n^2 + (977923/180)*n + (19746049/360).
EXAMPLE
Some solutions for n=4:
..0..0..0..1..1....0..0..0..1..1....1..1..0..0..0....0..1..0..0..1
..0..0..0..0..0....0..0..1..0..1....0..0..0..1..0....1..0..0..0..1
..0..0..0..0..1....0..0..0..0..1....0..0..0..0..1....1..0..1..1..1
..1..1..1..1..1....1..1..1..1..0....1..1..1..1..1....1..0..0..0..0
..1..0..1..1..1....0..1..1..1..0....0..1..1..1..1....1..1..1..1..0
..1..0..1..1..0....0..1..1..0..1....1..1..0..0..1....0..1..0..1..1
CROSSREFS
Cf. A259006.
Sequence in context: A323803 A246736 A289858 * A259008 A256899 A079048
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jun 16 2015
STATUS
approved

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Last modified April 19 12:14 EDT 2024. Contains 371792 sequences. (Running on oeis4.)