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A234227
T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).
9
104, 436, 436, 1824, 1560, 1824, 7696, 5612, 5612, 7696, 32384, 20724, 17448, 20724, 32384, 137536, 76972, 56936, 56936, 76972, 137536, 582144, 293316, 188040, 167688, 188040, 293316, 582144, 2488576, 1123724, 648536, 503272, 503272, 648536
OFFSET
1,1
Table starts
104 436 1824 7696 32384 137536 582144
436 1560 5612 20724 76972 293316 1123724
1824 5612 17448 56936 188040 648536 2264904
7696 20724 56936 167688 503272 1597896 5162984
32384 76972 188040 503272 1379816 4055128 12178344
137536 293316 648536 1597896 4055128 11145960 31418264
582144 1123724 2264904 5162984 12178344 31418264 83324136
2488576 4410276 8215256 17479656 38671960 94267656 236748824
10594304 17381356 30142344 60126376 125308904 289507096 690049704
45577216 70026180 114224792 215032104 425135512 935746056 2128516184
FORMULA
Empirical for column k (the k=4 recurrence also works for k=1..3; apparently the same order 16 recurrence works for all rows and columns):
k=1: a(n) = 4*a(n-1) +20*a(n-2) -80*a(n-3).
k=2: a(n) = 7*a(n-1) +20*a(n-2) -224*a(n-3) +144*a(n-4) +1680*a(n-5) -2880*a(n-6).
k=3: [order 11].
k=4: [order 16].
k=5: [same order 16].
k=6: [same order 16].
k=7: [same order 16].
EXAMPLE
Some solutions for n=4, k=4:
0 0 2 0 2 4 1 3 1 3 1 1 2 0 1 3 1 0 1 0
0 3 2 3 2 4 4 3 4 3 1 4 2 3 1 1 2 4 2 4
0 0 2 0 2 1 4 0 4 0 2 2 3 1 2 3 1 0 1 0
1 4 3 4 3 4 4 3 4 3 0 3 1 2 0 3 4 0 4 0
4 4 0 4 0 4 1 3 1 3 2 2 3 1 2 0 4 3 4 3
CROSSREFS
Sequence in context: A220063 A135441 A188150 * A234220 A234208 A372294
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 21 2013
STATUS
approved

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Last modified September 19 23:07 EDT 2024. Contains 376015 sequences. (Running on oeis4.)