A213697 -id:A213697 - cp's OEIS frontend

A213690 Half the number of (n+1)X(n+1) symmetric 0..1 arrays with no 2X2 subblock summing to 2.

3, 13, 70, 529, 5148, 68798, 1220409, 29377751, 949700962, 41536397680, 2450653487731, 195553849371916, 21091722699002539, 3077853629320011499, 607688763160596614184, 162407853243770174812161

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Column 1 of A213697

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

R. H. Hardin, Table of n, a(n) for n = 1..18

A213698 Half the number of 3 X 3 0..n symmetric arrays with no 2 X 2 subblock summing to 2n.

Original entry on oeis.org

13, 192, 1320, 5470, 17499, 45892, 105856, 219564, 421825, 758560, 1296408, 2117882, 3336655, 5087460, 7549184, 10927192, 15486741, 21525024, 29417800, 39578070, 52519203, 68796772, 89091840, 114132100, 144799369, 182025792

Offset: 1

R. H. Hardin, Jun 18 2012

nonn

Row 2 of A213697.

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

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

Cf. A213697.

Empirical: a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11).

Empirical g.f.: x*(13 + 153*x + 731*x^2 + 1461*x^3 + 1803*x^4 + 1111*x^5 + 425*x^6 + 59*x^7 + 4*x^8) / ((1 - x)^7*(1 + x)^4). - Colin Barker, Jul 22 2018

A213699 Half the number of 4X4 0..n symmetric arrays with no 2X2 subblock summing to 2n.

Original entry on oeis.org

70, 7827, 208072, 2322599, 16537086, 84059234, 342943680, 1169405354, 3500184570, 9372540629, 23022951048, 52423261153, 112270651514, 227577256564, 440658095360, 818409534692, 1466948929086, 2544850623111, 4291394833480

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Row 3 of A213697

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

R. H. Hardin, Table of n, a(n) for n = 1..144

Empirical: a(n) = 3*a(n-1) +5*a(n-2) -23*a(n-3) -4*a(n-4) +76*a(n-5) -28*a(n-6) -140*a(n-7) +98*a(n-8) +154*a(n-9) -154*a(n-10) -98*a(n-11) +140*a(n-12) +28*a(n-13) -76*a(n-14) +4*a(n-15) +23*a(n-16) -5*a(n-17) -3*a(n-18) +a(n-19)

A213700 Half the number of 5X5 0..n symmetric arrays with no 2X2 subblock summing to 2n.

Original entry on oeis.org

529, 750261, 109820000, 4286833981, 83545858925, 976919547736, 8159542628448, 51964311225934, 271341777491743, 1197645088919101, 4637119560078960, 16013821321719463, 50395763900241707, 145985579644461562

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Row 4 of A213697

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

R. H. Hardin, Table of n, a(n) for n = 1..33

A213701 Half the number of 6X6 0..n symmetric arrays with no 2X2 subblock summing to 2n.

Original entry on oeis.org

5148, 168382284, 193946752094, 34389632236877, 2256314178023600, 72037480156866493, 1425762604012263360, 19265705246048238885, 196522537519121864954, 1582723194473524459497, 10592676749133340851406

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Row 5 of A213697

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

R. H. Hardin, Table of n, a(n) for n = 1..15

A213702 Half the number of 7X7 0..n symmetric arrays with no 2X2 subblock summing to 2n.

Original entry on oeis.org

68798, 88681187619, 1146407046198040, 1199143411128185584, 325754552781442854792, 33704464361612549676417, 1829651398830137742302620, 59594337869095766240501287, 1329775905386553460207679334

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Row 6 of A213697

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

R. H. Hardin, Table of n, a(n) for n = 1..10

A213691 Half the number of (n+1)X(n+1) symmetric 0..2 arrays with no 2X2 subblock summing to 4.

Original entry on oeis.org

11, 192, 7827, 750261, 168382284, 88681187619, 109492322533385, 317058871268862262, 2152886481426876004067, 34281579489759899253123057, 1280103594445094955653155909620, 112093309434087933528612875492895053

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Column 2 of A213697

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

A213692 Half the number of (n+1) X (n+1) symmetric 0..3 arrays with no 2 X 2 subblock summing to 6.

Original entry on oeis.org

28, 1320, 208072, 109820000, 193946752094, 1146407046198040, 22678299640600736258, 1501445596428593204920908, 332684482425964910985336666019, 246706401290583205383638262307956104

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Column 3 of A213697.

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

Cf. A213697.

A213693 Half the number of (n+1) X (n+1) symmetric 0..4 arrays with no 2 X 2 subblock summing to 8.

Original entry on oeis.org

56, 5470, 2322599, 4286833981, 34389632236877, 1199143411128185584, 181744271406372884215557, 119728593804039164010819562504

Offset: 1

R. H. Hardin, Jun 18 2012

nonn

Column 4 of A213697.

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

Cf. A213697.

A213694 Half the number of (n+1)X(n+1) symmetric 0..5 arrays with no 2X2 subblock summing to 10.

Original entry on oeis.org

99, 17499, 16537086, 83545858925, 2256314178023600, 325754552781442854792, 251417716503635583550380605

Offset: 1

R. H. Hardin Jun 18 2012

nonn

Column 5 of A213697

			Some solutions for n=4
..1..4..4..1..0....3..3..2..3..3....2..4..3..0..4....2..3..1..0..3
..4..3..1..5..2....3..3..0..4..1....4..4..1..3..5....3..3..2..2..4
..4..1..0..3..3....2..0..3..4..4....3..1..5..2..2....1..2..5..0..0
..1..5..3..2..3....3..4..4..0..5....0..3..2..2..3....0..2..0..2..3
..0..2..3..3..5....3..1..4..5..2....4..5..2..3..3....3..4..0..3..3

cp's OEIS Frontend

A213690 Half the number of (n+1)X(n+1) symmetric 0..1 arrays with no 2X2 subblock summing to 2.

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A213698 Half the number of 3 X 3 0..n symmetric arrays with no 2 X 2 subblock summing to 2n.

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A213699 Half the number of 4X4 0..n symmetric arrays with no 2X2 subblock summing to 2n.

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A213700 Half the number of 5X5 0..n symmetric arrays with no 2X2 subblock summing to 2n.

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A213701 Half the number of 6X6 0..n symmetric arrays with no 2X2 subblock summing to 2n.

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A213702 Half the number of 7X7 0..n symmetric arrays with no 2X2 subblock summing to 2n.

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A213691 Half the number of (n+1)X(n+1) symmetric 0..2 arrays with no 2X2 subblock summing to 4.

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A213692 Half the number of (n+1) X (n+1) symmetric 0..3 arrays with no 2 X 2 subblock summing to 6.

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Crossrefs

A213693 Half the number of (n+1) X (n+1) symmetric 0..4 arrays with no 2 X 2 subblock summing to 8.

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Comments

Examples

Crossrefs

A213694 Half the number of (n+1)X(n+1) symmetric 0..5 arrays with no 2X2 subblock summing to 10.

Views

Author

Keywords

Comments

Examples