A213800 -id:A213800 - cp's OEIS frontend

A213793 Number of n X n 0..1 symmetric arrays with every row summing to floor(n/2).

1, 1, 2, 4, 18, 112, 1760, 35150, 1944530, 133948836, 26615510712, 6549149852112, 4762109992158288, 4274712091685443584, 11528251571501588791296, 38295413179145036856212700, 386860001875783390762182911250, 4805622573099374975572752075805000

Offset: 0

R. H. Hardin, Jun 20 2012

nonn

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

Andrew Howroyd, Table of n, a(n) for n = 0..24

Column 1 of A213800.

Cf. A333164.

a(2*n) = A333164(n). - Andrew Howroyd, Apr 08 2020

a(0)=1 prepended and terms a(13) and beyond from Andrew Howroyd, Apr 08 2020

A213801 Number of 3 X 3 0..n symmetric arrays with all rows summing to floor(n*3/2).

Original entry on oeis.org

4, 13, 29, 57, 96, 153, 226, 323, 440, 587, 759, 967, 1204, 1483, 1796, 2157, 2556, 3009, 3505, 4061, 4664, 5333, 6054, 6847, 7696, 8623, 9611, 10683, 11820, 13047, 14344, 15737, 17204, 18773, 20421, 22177, 24016, 25969, 28010, 30171, 32424, 34803, 37279

Offset: 1

R. H. Hardin, Jun 20 2012

nonn

Row 3 of A213800.

Sequence is difference between numbers of triangles, regardless of size, in A064412 (a family of ((3*n^2+3*n+2)/2)-iamonds, see also illustration of initial terms there) and a quantity A077043 of triangles of dimension 1. - Luce ETIENNE, Aug 23 2014

			Some solutions for n=4:
..1..3..2....2..4..0....0..4..2....1..2..3....1..1..4....4..0..2....2..2..2
..3..1..2....4..0..2....4..0..2....2..2..2....1..3..2....0..2..4....2..2..2
..2..2..2....0..2..4....2..2..2....3..2..1....4..2..0....2..4..0....2..2..2
a(2)=5-1=4, a(3)=14-1=13, a(210)=4118206-8269=4109937. - _Luce ETIENNE_, Aug 23 2014

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

Cf. A064412, A077403.

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-7) -a(n-8).
Empirical: G.f. -x*(-4-5*x-3*x^2-7*x^3-x^5-2*x^6+x^7) / ( (x^2+1)*(1+x)^2*(x-1)^4 ). - R. J. Mathar, Jul 04 2012
a(n) = (14*n^3+42*n^2+53*n+25+3*(n+1)*(-1)^n+2*((-1)^((2*n+1-(-1)^n)/4)-(-1)^((6*n+5-(-1)^n)/4)))/32. - Luce ETIENNE, Aug 23 2014
a(n) = A064412(n+1) - A077043((2*n+1-(-1)^n)/4). - Luce ETIENNE, Aug 23 2014

A213802 Number of 4X4 0..n symmetric arrays with all rows summing to 2*n.

Original entry on oeis.org

18, 169, 880, 3249, 9522, 23753, 52544, 106009, 198770, 351233, 590832, 953625, 1485778, 2245489, 3304704, 4751377, 6691410, 9251257, 12580080, 16852705, 22271986, 29072121, 37521216, 47924969, 60629426, 76025041, 94549616

Offset: 1

R. H. Hardin Jun 20 2012

nonn

Row 4 of A213800

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

R. H. Hardin, Table of n, a(n) for n = 1..173

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

Empirical: G.f. -x*(18+97*x+258*x^2+380*x^3+266*x^4+86*x^5+22*x^6+4*x^7-4*x^8+x^9) / ( (1+x)^3*(x-1)^7 ). - R. J. Mathar, Jul 04 2012

A213803 Number of 5 X 5 0..n symmetric arrays with all rows summing to floor(n*5/2).

Original entry on oeis.org

112, 5673, 87932, 815263, 4843626, 22698959, 84662388, 275879169, 782758404, 2036181209, 4827542558, 10773876919, 22498928491, 44939366943, 85390966217, 156814686053, 276999175867, 476278194021, 793826178700, 1294496520831

Offset: 1

R. H. Hardin, Jun 20 2012

nonn

Row 5 of A213800.

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

R. H. Hardin, Table of n, a(n) for n = 1..23

Cf. A213800.

A213792 Number of n X n 0..n symmetric arrays with every row summing to floor(n^2/2).

Original entry on oeis.org

1, 1, 3, 29, 3249, 4843626, 138198204339, 87098380004205128, 1525223999399549983474977

Offset: 0

R. H. Hardin, Jun 20 2012

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

Diagonal of A213800.

a(0)=1 prepended and a(7)-a(8) from Andrew Howroyd, Apr 07 2020

A213794 Number of n X n 0..2 symmetric arrays with every row summing to n.

Original entry on oeis.org

1, 1, 3, 13, 169, 5673, 526443, 133721189, 95133854529, 190409704025737, 1081810465812816481, 17533275809917986947451, 814583187343481957681992873, 108889213625061640897043875544377, 42017261328544343771207789776696995237, 46930798910194830781686389018692804741926963

Offset: 0

R. H. Hardin, Jun 20 2012

nonn

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

Column 2 of A213800.

a(0)=1 prepended and terms a(10) and beyond from Andrew Howroyd, Apr 07 2020

A213795 Number of n X n 0..3 symmetric arrays with every row summing to floor(n*3/2).

Original entry on oeis.org

1, 1, 4, 29, 880, 87932, 34725760, 46259653191, 250599609089536, 4664255347861848000, 359514810915617810737152, 96221422835240936091862618254, 107926925135028470351157750883132800, 423270762332675097186733226425581010359872

Offset: 0

R. H. Hardin, Jun 20 2012

nonn

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

Column 3 of A213800.

a(0)=1 prepended and terms a(9) and beyond from Andrew Howroyd, Apr 07 2020

A213796 Number of n X n 0..4 symmetric arrays with every row summing to 2*n.

Original entry on oeis.org

1, 1, 5, 57, 3249, 815263, 932587453, 4893373431575, 119570350092328225, 13715276642286471266345, 7439775168632414842497242951, 19190656372074846793620422063221831, 236483103820478991417179706813598595965425

Offset: 0

R. H. Hardin, Jun 20 2012

nonn

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

Column 4 of A213800.

a(0)=1 prepended and a(8)-a(12) from Andrew Howroyd, Apr 07 2020

A213797 Number of n X n 0..5 symmetric arrays with every row summing to floor(n*5/2).

Original entry on oeis.org

1, 6, 96, 9522, 4843626, 13937940952, 212962858290086

Offset: 1

R. H. Hardin Jun 20 2012

nonn

Column 5 of A213800

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

A213798 Number of n X n 0..6 symmetric arrays with every row summing to 3*n.

Original entry on oeis.org

1, 7, 153, 23753, 22698959, 138198204339

Offset: 1

R. H. Hardin Jun 20 2012

nonn

Column 6 of A213800

			Some solutions for n=4
..3..1..2..6....0..0..6..6....0..3..3..6....6..6..0..0....3..5..1..3
..1..5..2..4....0..5..1..6....3..4..4..1....6..2..3..1....5..6..0..1
..2..2..6..2....6..1..5..0....3..4..1..4....0..3..3..6....1..0..5..6
..6..4..2..0....6..6..0..0....6..1..4..1....0..1..6..5....3..1..6..2

cp's OEIS Frontend

A213793 Number of n X n 0..1 symmetric arrays with every row summing to floor(n/2).

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A213801 Number of 3 X 3 0..n symmetric arrays with all rows summing to floor(n*3/2).

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A213802 Number of 4X4 0..n symmetric arrays with all rows summing to 2*n.

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A213803 Number of 5 X 5 0..n symmetric arrays with all rows summing to floor(n*5/2).

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A213792 Number of n X n 0..n symmetric arrays with every row summing to floor(n^2/2).

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A213794 Number of n X n 0..2 symmetric arrays with every row summing to n.

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A213795 Number of n X n 0..3 symmetric arrays with every row summing to floor(n*3/2).

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A213796 Number of n X n 0..4 symmetric arrays with every row summing to 2*n.

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A213797 Number of n X n 0..5 symmetric arrays with every row summing to floor(n*5/2).

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A213798 Number of n X n 0..6 symmetric arrays with every row summing to 3*n.

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