A203656 -id:A203656 - cp's OEIS frontend

A203650 1/25 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

81, 1517, 28057, 519445, 9616161, 178019197, 3295578857, 61009378085, 1129435635441, 20908668388877, 387071560403257, 7165659241743925, 132654210800937921, 2455760042384774557, 45462238622967429257

Offset: 1

R. H. Hardin, Jan 04 2012

nonn

Column 2 of A203656.

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

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

Cf. A203656.

Empirical: a(n) = 17*a(n-1) +28*a(n-2).
Conjectures from Colin Barker, Jun 04 2018: (Start)
G.f.: x*(81 + 140*x) / (1 - 17*x - 28*x^2).
a(n) = (2^(-1-n)*((17-sqrt(401))^n*(-77+5*sqrt(401)) + (17+sqrt(401))^n*(77+5*sqrt(401))))/sqrt(401).
(End)

A203651 1/25 the number of (n+1) X 4 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

729, 28057, 1116249, 44577561, 1780968921, 71156938905, 2843024036697, 113591039131161, 4538450923550937, 181330649884558233, 7244939996157320793, 289466538539290446105, 11565434217440894223321, 462088880162456091840153

Offset: 1

R. H. Hardin, Jan 04 2012

nonn

Column 3 of A203656.

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

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

Cf. A203656.

Empirical: a(n) = 45*a(n-1) -204*a(n-2) +96*a(n-3).

Empirical g.f.: x*(729 - 4748*x + 2400*x^2) / (1 - 45*x + 204*x^2 - 96*x^3). - Colin Barker, Jun 04 2018

A203652 1/25 the number of (n+1)X5 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

6561, 519445, 44577561, 3906948333, 343812029649, 30292030417413, 2669260624372937, 235230466316286557, 20729666228601067777, 1826821038860074533877, 160989718241260912957305

Offset: 1

R. H. Hardin Jan 04 2012

nonn

Column 4 of A203656

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

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

Empirical: a(n) = 69*a(n-1) +2528*a(n-2) -75120*a(n-3) +59456*a(n-4) +1531904*a(n-5) -345088*a(n-6) -1646592*a(n-7)

A203653 1/25 the number of (n+1)X6 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

59049, 9616161, 1780968921, 343812029649, 67213191427593, 13192335511091073, 2592476403527692089, 509649251749126118193, 100202323670442739140969, 19701512822564218199726049, 3873700712374667692894221465

Offset: 1

R. H. Hardin Jan 04 2012

nonn

Column 5 of A203656

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

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

Empirical: a(n) = 249*a(n-1) -8592*a(n-2) -421104*a(n-3) +17434560*a(n-4) -117447936*a(n-5) -1126380544*a(n-6) +12165427200*a(n-7) -13434667008*a(n-8) -89049268224*a(n-9) +101291655168*a(n-10) +94447337472*a(n-11) -82896224256*a(n-12)

A203654 1/25 the number of (n+1)X7 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

531441, 178019197, 71156938905, 30292030417413, 13192335511091073, 5796397762880763341, 2554890395768832271017, 1127594169687376371159253, 497870086469175871336506385, 219871060492143544799371582749

Offset: 1

R. H. Hardin Jan 04 2012

nonn

Column 6 of A203656

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

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

Empirical: a(n) = 329*a(n-1) +107668*a(n-2) -25063968*a(n-3) -680298432*a(n-4) +202122434560*a(n-5) +566048790528*a(n-6) -556012878114816*a(n-7) +3504577252474880*a(n-8) +591608256378830848*a(n-9) -6839009506476949504*a(n-10) -239163894638688862208*a(n-11) +3525511542366864932864*a(n-12) +35450315597944711020544*a(n-13) -664062013074729355706368*a(n-14) -1530140375300205031981056*a(n-15) +50183396342386988796608512*a(n-16) -17094562720050709209808896*a(n-17) -1622789056358547469740539904*a(n-18) +2031702560273665184466206720*a(n-19) +21489007078579909036995510272*a(n-20) -30394434853378035268349591552*a(n-21) -101547952483445807369349496832*a(n-22) +114461568017537120233548939264*a(n-23) +177927593591172462047265816576*a(n-24) -114513709337590944825725681664*a(n-25) -72325116345546289517124648960*a(n-26) +34013569597018368539319336960*a(n-27) -3061173118029560521791897600*a(n-28)

A203655 1/25 the number of (n+1)X8 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

4782969, 3295578857, 2843024036697, 2669260624372937, 2592476403527692089, 2554890395768832271017, 2533535485859974387986201, 2519204090844384026262668425, 2507880611006135260374020018937

Offset: 1

R. H. Hardin Jan 04 2012

nonn

Column 7 of A203656

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

R. H. Hardin, Table of n, a(n) for n = 1..22

A203649 1/25 the number of (n+1) X (n+1) 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

9, 1517, 1116249, 3906948333, 67213191427593, 5796397762880763341

Offset: 1

R. H. Hardin, Jan 04 2012

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

Diagonal of A203656.

cp's OEIS Frontend

A203650 1/25 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

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A203651 1/25 the number of (n+1) X 4 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

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A203652 1/25 the number of (n+1)X5 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

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A203653 1/25 the number of (n+1)X6 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

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A203654 1/25 the number of (n+1)X7 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

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A203655 1/25 the number of (n+1)X8 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

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A203649 1/25 the number of (n+1) X (n+1) 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

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Examples

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