cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A206391 Number of n X 3 0..5 arrays with no element equal to another within a city block distance of two, and new values 0..5 introduced in row major order.

Original entry on oeis.org

1, 4, 26, 206, 1592, 12428, 96632, 752552, 5856992, 45595664, 354918176, 2762807264, 21506309504, 167411006144, 1303169775488, 10144214859392, 78965192918528, 614685592164608, 4784872150020608, 37246687385693696
Offset: 1

Views

Author

R. H. Hardin, Feb 07 2012

Keywords

Comments

Column 3 of A206396.

Examples

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

Crossrefs

Cf. A206396.

Formula

Empirical: a(n) = 6*a(n-1) + 18*a(n-2) - 32*a(n-3) for n>5.
Empirical g.f.: x*(1 - 2*x - 16*x^2 + 10*x^3 + 16*x^4) / (1 - 6*x - 18*x^2 + 32*x^3). - Colin Barker, Jun 16 2018

A206392 Number of n X 4 0..5 arrays with no element equal to another within a city block distance of two, and new values 0..5 introduced in row major order.

Original entry on oeis.org

2, 25, 206, 1931, 16784, 151630, 1343560, 12046648, 107401612, 960610876, 8576723918, 76644197120, 684569775162, 6116039277778, 54633888067900, 488076198634430, 4360092827131800, 38950530867108738, 347957262094712236
Offset: 1

Views

Author

R. H. Hardin, Feb 07 2012

Keywords

Comments

Column 4 of A206396.

Examples

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

Crossrefs

Cf. A206396.

Formula

Empirical: a(n) = 14*a(n-1) -32*a(n-2) -281*a(n-3) +1738*a(n-4) -1728*a(n-5) -9767*a(n-6) +21963*a(n-7) -7410*a(n-8) +5706*a(n-9) -19704*a(n-10) +6028*a(n-11) +2512*a(n-12) -2176*a(n-13) for n>15.

A206393 Number of nX5 0..5 arrays with no element equal to another within a city block distance of two, and new values 0..5 introduced in row major order.

Original entry on oeis.org

5, 172, 1592, 16784, 170796, 1787258, 18574298, 193499878, 2014220262, 20973561786, 218384365724, 2274041419152, 23679689583822, 246582133806618, 2567714799158370, 26738384205646006, 278434494273903426
Offset: 1

Views

Author

R. H. Hardin Feb 07 2012

Keywords

Comments

Column 5 of A206396

Examples

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

Formula

Empirical: a(n) = 19*a(n-1) -28*a(n-2) -1368*a(n-3) +6837*a(n-4) +30894*a(n-5) -259715*a(n-6) -158240*a(n-7) +4305294*a(n-8) -2907345*a(n-9) -36456187*a(n-10) +17700441*a(n-11) +264833772*a(n-12) +359253348*a(n-13) -3077852142*a(n-14) -4085375360*a(n-15) +29632825925*a(n-16) +13040334064*a(n-17) -175557464522*a(n-18) -60798023894*a(n-19) +1054573134761*a(n-20) +156059590354*a(n-21) -7365833614192*a(n-22) +9642172417687*a(n-23) +18919359102713*a(n-24) -74981349795094*a(n-25) +77760958965261*a(n-26) +59754494935940*a(n-27) -287857949600101*a(n-28) +691064089663409*a(n-29) -956324740445126*a(n-30) -738343162745785*a(n-31) +3909998344750953*a(n-32) -3355221285631341*a(n-33) -1701316400605256*a(n-34) +3179682162276913*a(n-35) -270478484532986*a(n-36) -5293044447668192*a(n-37) +25344266042370966*a(n-38) -28784566717360175*a(n-39) -17947836174493735*a(n-40) +67609956522748602*a(n-41) -101102908627491482*a(n-42) +104803692847485310*a(n-43) -57693328594689530*a(n-44) -10870560756068936*a(n-45) +69553561235094500*a(n-46) -80973326026485056*a(n-47) +47246917468719560*a(n-48) -11386765181702208*a(n-49) -2931176567684912*a(n-50) +4099580409184672*a(n-51) -2335307914381056*a(n-52) +605917226114688*a(n-53) +41498237271040*a(n-54) -93505834844160*a(n-55) +25819492058112*a(n-56) +690971830272*a(n-57) -51588218880*a(n-58) +2691366912*a(n-59) for n>63

A206394 Number of nX6 0..5 arrays with no element equal to another within a city block distance of two, and new values 0..5 introduced in row major order.

Original entry on oeis.org

15, 1201, 12428, 151630, 1787258, 21983256, 268956972, 3301485294, 40603817198, 499201392028, 6147736324286, 75698270712532, 932481394642188, 11487787221488608, 141538253304943642, 1744036023952329892
Offset: 1

Views

Author

R. H. Hardin Feb 07 2012

Keywords

Comments

Column 6 of A206396

Examples

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

A206390 Number of n X n 0..5 arrays with no element equal to another within a city block distance of two, and new values 0..5 introduced in row major order.

Original entry on oeis.org

1, 1, 26, 1931, 170796, 21983256, 3889732730, 998388746378
Offset: 1

Views

Author

R. H. Hardin Feb 07 2012

Keywords

Comments

Diagonal of A206396.

Examples

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

Crossrefs

Cf. A206396.

A206395 Number of nX7 0..5 arrays with no element equal to another within a city block distance of two, and new values 0..5 introduced in row major order.

Original entry on oeis.org

51, 8404, 96632, 1343560, 18574298, 268956972, 3889732730, 56960076094, 835640037768, 12318524591500
Offset: 1

Views

Author

R. H. Hardin Feb 07 2012

Keywords

Comments

Column 7 of A206396

Examples

			Some solutions for n=4
..0..1..2..0..1..2..3....0..1..2..3..4..0..1....0..1..2..3..0..1..2
..2..3..4..5..3..4..5....2..3..5..0..1..2..4....2..3..4..1..5..3..4
..4..5..1..2..0..1..2....5..4..1..2..5..3..0....4..5..0..2..4..0..5
..0..2..3..4..5..3..4....0..2..3..4..0..1..5....0..1..3..5..1..2..3
		
Showing 1-6 of 6 results.