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A235280 T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant stress 1X1 tilings) 11
40, 100, 100, 208, 208, 208, 520, 380, 380, 520, 1120, 844, 632, 844, 1120, 2800, 1660, 1280, 1280, 1660, 2800, 6208, 3844, 2344, 2344, 2344, 3844, 6208, 15520, 8012, 5096, 3952, 3952, 5096, 8012, 15520, 35200, 19060, 10088, 7936, 6232, 7936, 10088, 19060 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....40....100....208....520...1120...2800...6208..15520..35200...88000..203008

...100....208....380....844...1660...3844...8012..19060..41500..100468..225740

...208....380....632...1280...2344...5096..10088..23000..48328..113720..249512

...520....844...1280...2344...3952...7936..14672..31504..62800..141424..298640

..1120...1660...2344...3952...6232..11704..20440..41704..79480..172360..352024

..2800...3844...5096...7936..11704..20440..33464..64168.115480..238024..463736

..6208...8012..10088..14672..20440..33464..51800..93992.160888..317192..593048

.15520..19060..23000..31504..41704..64168..93992.160888.260680..487960..867560

.35200..41500..48328..62800..79480.115480.160888.260680.401560..716200.1215928

.88000.100468.113720.141424.172360.238024.317192.487960.716200.1215928.1966280

Empirical: T(n,k)=Number of (n+1)X(k+1) 0..3+i arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 3+2*i, for i=1..3(..?)

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..420

FORMULA

Empirical for column k (the k=2..9 recurrence also works for k=1; apparently all rows and columns satisfy the same order 9 recurrence):

diagonal: [linear recurrence of order 11, computed assuming that all rows and columns satisfy the same order 9 recurrence]

k=1: a(n) = 10*a(n-2) -24*a(n-4)

k=2..9: [same order 9 recurrence]

EXAMPLE

Some solutions for n=4 k=4

..3..1..2..1..3....1..2..1..2..0....4..1..4..3..4....1..3..2..3..0

..1..4..0..4..1....4..0..4..0..3....0..2..0..4..0....3..0..4..0..2

..4..2..3..2..4....3..4..3..4..2....4..1..4..3..4....2..4..3..4..1

..1..4..0..4..1....4..0..4..0..3....0..2..0..4..0....3..0..4..0..2

..3..1..2..1..3....1..2..1..2..0....3..0..3..2..3....1..3..2..3..0

CROSSREFS

Sequence in context: A211493 A185791 A092889 * A235271 A033832 A235017

Adjacent sequences:  A235277 A235278 A235279 * A235281 A235282 A235283

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 05 2014

STATUS

approved

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)