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A204651 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively 9
8, 16, 16, 28, 32, 28, 48, 56, 56, 48, 80, 90, 104, 90, 80, 132, 137, 178, 178, 137, 132, 216, 200, 284, 330, 284, 200, 216, 352, 283, 434, 571, 571, 434, 283, 352, 572, 390, 637, 938, 1076, 938, 637, 390, 572, 928, 526, 908, 1478, 1918, 1918, 1478, 908, 526, 928 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...8..16..28...48...80...132...216...352...572....928...1504...2436...3944

..16..32..56...90..137...200...283...390...526....696....906...1162...1471

..28..56.104..178..284...434...637...908..1259...1708...2270...2966...3814

..48..90.178..330..571...938..1478..2248..3317...4766...6690...9198..12415

..80.137.284..571.1076..1918..3261..5329..8408..12867..19162..27859..39640

.132.200.434..938.1918..3702..6780.11868.19969..32450..51134..78404.117324

.216.283.637.1478.3261..6780.13314.24862.44426..76378.126906.204583.321038

.352.390.908.2248.5329.11868.24862.49312.93219.168960.295101.498776.818748

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..6956

FORMULA

Empirical: T(n,k) recurrences

T(1,k)=2*T(1,k-1)-T(1,k-3)

T(2,k)=4*T(2,k-1)-5*T(2,k-2)+5*T(2,k-4)-4*T(2,k-5)+T(2,k-6)

T(3,k)=4*T(3,k-1)-5*T(3,k-2)+5*T(3,k-4)-4*T(3,k-5)+T(3,k-6) for k>7

T(4,k)=5*T(4,k-1)-9*T(4,k-2)+5*T(4,k-3)+5*T(4,k-4)-9*T(4,k-5)+5*T(4,k-6)-T(4,k-7) for k>9

and in general for n>2 (checked to n=15 k=210):

row recurrence coefficients are the coefficients of (1+x)*(1-x)^(k+2) and the row recurrence is valid for k>2*n+1

EXAMPLE

Some solutions for n=5 k=3

..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..1

..0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1

..0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1

..0..0..1..1....0..0..1..1....0..0..0..1....0..0..0..1....0..0..1..1

..0..0..1..1....1..1..1..1....0..0..0..1....0..0..0..1....0..1..1..1

..0..0..1..1....1..1..1..1....1..1..1..0....0..1..1..1....0..1..1..1

CROSSREFS

Sequence in context: A040056 A242890 A224550 * A203452 A319317 A091251

Adjacent sequences:  A204648 A204649 A204650 * A204652 A204653 A204654

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jan 17 2012

STATUS

approved

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Last modified September 25 12:12 EDT 2022. Contains 356984 sequences. (Running on oeis4.)