A200454 -id:A200454 - cp's OEIS frontend

A200448 Number of -2..2 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

10, 44, 144, 486, 1582, 5478, 18692, 64782, 223272, 776430, 2701660, 9439702, 33021250, 115801892, 406698282, 1430840312, 5040451088, 17779563894, 62784860258, 221948186878, 785340477204, 2781302241584, 9857972484436

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 2 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..200

A200449 Number of -3..3 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

26, 142, 728, 3788, 19802, 103726, 548204, 2916664, 15576706, 83481240, 448758338, 2418733790, 13066215896, 70726653732, 383520053994, 2082953525918, 11328873637896, 61694898371006, 336368349457684, 1835858710497508

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 3 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..200

A200450 Number of -4..4 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

44, 342, 2334, 16380, 115140, 820650, 5876818, 42324384, 306098316, 2222013090, 16179361028, 118122171194, 864377954818, 6338065287424, 46557302873890, 342540516750538, 2523812868946712, 18619248362911724, 137522653687668252

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 4 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..200

A200451 Number of -5..5 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

72, 678, 5720, 50852, 451708, 4062384, 36725772, 334032710, 3050654456, 27965763262, 257160791680, 2371128350480, 21913699015614, 202938626310668, 1882772669652668, 17495621074794634, 162811923678190584

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 5 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..158

A200452 Number of -6..6 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

102, 1148, 12002, 127988, 1375006, 14923636, 163058296, 1791564880, 19771609900, 219008350922, 2433568582846, 27114470656254, 302815705130546, 3388823734521446, 37993433832232370, 426648365048068166

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 6 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..119

A200453 Number of -7..7 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

142, 1832, 22276, 278906, 3513884, 44716536, 572857272, 7380022092, 95496980144, 1240352594210, 16161267003100, 211148128583658, 2765181621011902, 36287540439791446, 477071904597059874, 6282247056373911518

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 7 of A200454.

			Some solutions for n=3
.-1...-4....0....7....5....5....6...-4....2....0...-1...-5....4....2...-6...-6
.-3....3....2....0...-1....2...-2....6....3....4....2....6...-5....3...-1....7
..4....4...-5...-1...-2...-6...-4....4...-5...-1...-3....1....1...-4....1...-6
.-5...-3....3...-4...-4...-4...-7....0...-1...-4....4...-5...-3....3....6....2
..5....0....0...-2....2....3....7...-6....1....1...-2....3....3...-4....0....3

R. H. Hardin, Table of n, a(n) for n = 1..97

A200456 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

4, 44, 142, 342, 678, 1148, 1832, 2744, 3874, 5334, 7114, 9192, 11708, 14644, 17962, 21826, 26206, 31044, 36544, 42660, 49310, 56734, 64866, 73616, 83256, 93696, 104834, 116970, 130006, 143824, 158748, 174668, 191446, 209446, 228542, 248572

Offset: 1

R. H. Hardin, Nov 18 2011

nonn

Row 2 of A200454.

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A200454.

Empirical: a(n) = a(n-1) +2*a(n-3) -2*a(n-4) +a(n-5) -2*a(n-6) +a(n-7) -2*a(n-8) +2*a(n-9) +a(n-11) -a(n-12).

Empirical g.f.: 2*(1 + x)*(2 + 18*x + 31*x^2 + 65*x^3 + 63*x^4 + 72*x^5 + 52*x^6 + 39*x^7 + 9*x^8 + 9*x^9) / ((1 - x)^4*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 21 2018

A200457 Number of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

6, 144, 728, 2334, 5720, 12002, 22276, 38174, 61290, 93704, 137374, 194964, 268842, 362092, 477620, 618954, 789324, 992970, 1233412, 1515270, 1842742, 2220844, 2654034, 3148080, 3707758, 4339192, 5047836, 5840186, 6721964, 7700510, 8781768

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Row 3 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = -a(n-1) +a(n-3) +2*a(n-4) +2*a(n-5) +a(n-6) -a(n-8) -a(n-9) -a(n-10) -2*a(n-11) -2*a(n-12) -2*a(n-13) -a(n-14) +a(n-15) +2*a(n-16) +2*a(n-17) +2*a(n-18) +a(n-19) +a(n-20) +a(n-21) -a(n-23) -2*a(n-24) -2*a(n-25) -a(n-26) +a(n-28) +a(n-29)

A200458 Number of -n..n arrays x(0..5) of 6 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

10, 486, 3788, 16380, 50852, 127988, 278906, 547518, 991740, 1686602, 2726152, 4224676, 6319970, 9175294, 12980046, 17954222, 24348932, 32448240, 42572590, 55080404, 70369230, 88879322, 111095332, 137546940, 168813148, 205524308

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Row 4 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = a(n-3) +a(n-4) +2*a(n-5) -2*a(n-8) -a(n-9) -2*a(n-10) -a(n-11) -a(n-12) +2*a(n-15) +2*a(n-16) +2*a(n-17) +2*a(n-18) -a(n-21) -a(n-22) -2*a(n-23) -a(n-24) -2*a(n-25) +2*a(n-28) +a(n-29) +a(n-30) -a(n-33)

A200459 Number of -n..n arrays x(0..6) of 7 elements with zero sum and nonzero first and second differences.

Original entry on oeis.org

14, 1582, 19802, 115140, 451708, 1375006, 3513884, 7910100, 16176994, 30639164, 54582252, 92444962, 150029642, 234839570, 356372880, 526276044, 758938962, 1071722528, 1485196016, 2023848468, 2716453852, 3596089776, 4701336350

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Row 5 of A200454

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

R. H. Hardin, Table of n, a(n) for n = 1..96

cp's OEIS Frontend

A200448 Number of -2..2 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

A200449 Number of -3..3 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

A200450 Number of -4..4 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

A200451 Number of -5..5 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

A200452 Number of -6..6 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

A200453 Number of -7..7 arrays x(0..n+1) of n+2 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

A200456 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A200457 Number of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

Formula

A200458 Number of -n..n arrays x(0..5) of 6 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links

Formula

A200459 Number of -n..n arrays x(0..6) of 7 elements with zero sum and nonzero first and second differences.

Views

Author

Keywords

Comments

Examples

Links