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 1-10 of 10 results.

A199841 Number of -2..2 arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

1, 3, 8, 23, 66, 192, 575, 1739, 5307, 16304, 50381, 156408, 487398, 1523663, 4776107, 15006513, 47247134, 149023605, 470794024, 1489462276, 4718330397, 14964219411, 47509518289, 150982994162, 480243297965, 1528796563830, 4870415108094
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 2 of A199847

Examples

			Some solutions for n=6
..2...-1....2....1....2....1....1....1....1...-1....2....1....1....1....1....1
..1....0....0...-1....1....1....2....1...-1....0....2....1....1....2....0....0
.-2....1....1....0....2....0....0....0...-1....1...-2....1....1....1....0...-1
.-1....0...-2....0...-1...-1....0....1....0....1...-1....0...-1...-1....0....0
..0....1...-1....0...-2....0...-2...-2....0....1...-1...-1....0...-1....1....0
..0...-1....0....0...-2...-1...-1...-1....1...-2....0...-2...-2...-2...-2....0
		

A199842 Number of -3..3 arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

1, 4, 13, 42, 132, 428, 1393, 4561, 15032, 49889, 166542, 558744, 1883028, 6370957, 21628455, 73641852, 251385571, 860067894, 2948380732, 10124956970, 34823894885, 119940097035, 413612099138, 1427945022753, 4934850614704
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Column 3 of A199847.

Examples

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

A199843 Number of -4..4 arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

1, 5, 18, 68, 239, 845, 2958, 10349, 36111, 126121, 441161, 1546353, 5432430, 19130949, 67536934, 238991556, 847646318, 3012890719, 10730694626, 38289978058, 136865206035, 489995352710, 1756812943841, 6307268945198
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 4 of A199847

Examples

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

A199844 Number of -5..5 arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

1, 6, 25, 103, 399, 1532, 5754, 21383, 78735, 288580, 1053894, 3840866, 13981403, 50874249, 185128907, 673970102, 2455319377, 8952722626, 32676307483, 119391572211, 436711281979, 1599194641093, 5862625449021, 21515851244159
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Column 5 of A199847.

Examples

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

Crossrefs

Cf. A199847.

A199845 Number of -6..6 arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

1, 7, 32, 149, 630, 2600, 10426, 41079, 159330, 611698, 2329458, 8818874, 33234990, 124835120, 467743203, 1749482957, 6535398559, 24393753898, 91006458115, 339442473410, 1266045976128, 4722720042212, 17621749081077, 65775214030886
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 6 of A199847

Examples

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

A199846 Number of -7..7 arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

1, 8, 41, 206, 944, 4188, 17879, 74424, 303400, 1218440, 4833416, 18992142, 74057460, 287035502, 1107086841, 4253339267, 16289667330, 62230152461, 237255014892, 903101912666, 3433312226666, 13039708953325, 49488269035164
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 7 of A199847

Examples

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

A199848 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

11, 23, 42, 68, 103, 149, 206, 276, 361, 461, 578, 714, 869, 1045, 1244, 1466, 1713, 1987, 2288, 2618, 2979, 3371, 3796, 4256, 4751, 5283, 5854, 6464, 7115, 7809, 8546, 9328, 10157, 11033, 11958, 12934, 13961, 15041, 16176, 17366, 18613, 19919, 21284
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 4 of A199847.

Examples

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

Crossrefs

Cf. A199847.

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -3*a(n-4) +3*a(n-5) -a(n-6).
Empirical g.f.: x*(11 - 10*x + 6*x^2 - 11*x^3 + 12*x^4 - 4*x^5) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, May 16 2018

A199849 Number of -n..n arrays x(0..4) of 5 elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

26, 66, 132, 239, 399, 630, 944, 1367, 1913, 2612, 3482, 4557, 5857, 7424, 9278, 11465, 14011, 16966, 20356, 24239, 28643, 33630, 39232, 45515, 52513, 60300, 68910, 78421, 88873, 100348, 112886, 126577, 141463, 157638, 175148, 194091, 214515, 236526
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 5 of A199847.

Examples

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

Crossrefs

Cf. A199847.

Formula

Empirical: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11) for n>12.
Empirical g.f.: x*(26 + 14*x + x^3 - 13*x^4 + 16*x^5 + 3*x^6 + 10*x^7 - 3*x^8 - 16*x^9 + 7*x^10 + x^11) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 16 2018

A199850 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

63, 192, 428, 845, 1532, 2600, 4188, 6465, 9634, 13932, 19636, 27065, 36582, 48598, 63576, 82029, 104530, 131710, 164262, 202945, 248586, 302082, 364406, 436607, 519814, 615238, 724178, 848019, 988240, 1146414, 1324210, 1523399, 1745856
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 6 of A199847.

Examples

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

Crossrefs

Cf. A199847.

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-5) -a(n-6) -a(n-7) +2*a(n-8) -a(n-10) -2*a(n-11) +3*a(n-12) -a(n-13) for n>14.
Empirical g.f.: x*(63 + 3*x - 22*x^2 + 8*x^3 + 45*x^4 - 4*x^5 - 24*x^6 + 32*x^7 + 19*x^8 - 27*x^9 - 43*x^10 + 39*x^11 + 8*x^12 - 9*x^13) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 16 2018

A199851 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no element more than one greater than the previous.

Original entry on oeis.org

153, 575, 1393, 2958, 5754, 10426, 17879, 29268, 46126, 70322, 104253, 150764, 213380, 296204, 404213, 543086, 719592, 941366, 1217343, 1557506, 1973400, 2477778, 3085247, 3811830, 4675676, 5696580, 6896795, 8300422, 9934376
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Row 7 of A199847

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) -a(n-3) -a(n-5) +a(n-6) -2*a(n-7) +2*a(n-8) +a(n-9) -a(n-13) -2*a(n-14) +2*a(n-15) -a(n-16) +a(n-17) +a(n-19) -2*a(n-21) +a(n-22) for n>24
Showing 1-10 of 10 results.