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.

A200186 Number of -2..2 arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

1, 4, 6, 14, 24, 54, 104, 230, 464, 1028, 2128, 4720, 9918, 22038, 46760, 104056, 222338, 495358, 1064138, 2373070, 5119796, 11425974, 24738074, 55242788, 119958510, 268018844, 583462384, 1304179214, 2845288284, 6362293924
Offset: 1

Views

Author

R. H. Hardin Nov 14 2011

Keywords

Comments

Column 2 of A200192

Examples

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

A200187 Number of -3..3 arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

1, 6, 14, 48, 144, 482, 1534, 5148, 16826, 56918, 188706, 642300, 2149072, 7348408, 24749244, 84919630, 287439908, 988917344, 3360535304, 11586463472, 39498606276, 136421151864, 466287543690, 1612808711870, 5524756100592
Offset: 1

Views

Author

R. H. Hardin Nov 14 2011

Keywords

Comments

Column 3 of A200192

Examples

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

A200188 Number of -4..4 arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

1, 8, 28, 120, 506, 2240, 9856, 44562, 199932, 914676, 4152696, 19143782, 87622590, 406118090, 1869888346, 8701509206, 40245967276, 187867050760, 872020225984, 4080661245080, 18995817588580, 89071683414448, 415623180115020
Offset: 1

Views

Author

R. H. Hardin Nov 14 2011

Keywords

Comments

Column 4 of A200192

Examples

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

A200189 Number of -5..5 arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

1, 10, 44, 242, 1298, 7266, 40632, 231916, 1320876, 7630236, 43951298, 255926506, 1485664226, 8700154180, 50792100530, 298703878402, 1751415860436, 10333766393384, 60797757383394, 359661008763242, 2121869963574120
Offset: 1

Views

Author

R. H. Hardin Nov 14 2011

Keywords

Comments

Column 5 of A200192

Examples

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

A200190 Number of -6..6 arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

1, 12, 66, 426, 2794, 18838, 127800, 881008, 6081086, 42452472, 296258332, 2085263400, 14662923954, 103810065802, 734016517080, 5219300699654, 37060739113354, 264413563521598, 1883784631395118, 13476226807283384
Offset: 1

Views

Author

R. H. Hardin Nov 14 2011

Keywords

Comments

Column 6 of A200192

Examples

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

A200191 Number of -7..7 arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

1, 14, 90, 688, 5300, 41938, 334278, 2702398, 21910764, 179391752, 1470318926, 12138752566, 100237526220, 832451175714, 6911760321744, 57654489610890, 480698731253616, 4023489592590784, 33656450218770442, 282477294114249058
Offset: 1

Views

Author

R. H. Hardin Nov 14 2011

Keywords

Comments

Column 7 of A200192

Examples

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

A200193 Number of -n..n arrays x(0..3) of 4 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

2, 14, 48, 120, 242, 426, 688, 1040, 1494, 2066, 2768, 3612, 4614, 5786, 7140, 8692, 10454, 12438, 14660, 17132, 19866, 22878, 26180, 29784, 33706, 37958, 42552, 47504, 52826, 58530, 64632, 71144, 78078, 85450, 93272, 101556, 110318, 119570, 129324
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2011

Keywords

Comments

Row 4 of A200192.
4th difference is 0 4 -4 0 4 -4 0 4 -4 0 4 -4.

Examples

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

Crossrefs

Cf. A200192.

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.: 2*x*(1 + 3*x + x^2)*(1 + x + 2*x^2) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, May 20 2018

A200194 Number of -n..n arrays x(0..4) of 5 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

0, 24, 144, 506, 1298, 2794, 5300, 9220, 14974, 23094, 34120, 48712, 67524, 91346, 120950, 157254, 201146, 253672, 315838, 388820, 473738, 571896, 684534, 813084, 958900, 1123544, 1308488, 1515422, 1745934, 2001842, 2284852, 2596912, 2939842
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2011

Keywords

Comments

Row 5 of A200192.

Examples

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

Crossrefs

Cf. A200192.

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).
Empirical g.f.: 2*x^2*(12 + 48*x + 109*x^2 + 155*x^3 + 171*x^4 + 133*x^5 + 79*x^6 + 26*x^7 + 3*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 20 2018

A200195 Number of -n..n arrays x(0..5) of 6 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

2, 54, 482, 2240, 7266, 18838, 41938, 83600, 153278, 263198, 428718, 668684, 1005790, 1466934, 2083578, 2892104, 3934174, 5257082, 6914122, 8964936, 11475878, 14520370, 18179258, 22541172, 27702886, 33769670, 40855654, 49084180
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2011

Keywords

Comments

Row 6 of A200192.

Examples

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

Crossrefs

Cf. A200192.

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).
Empirical g.f.: 2*x*(1 + 24*x + 162*x^2 + 452*x^3 + 782*x^4 + 999*x^5 + 1045*x^6 + 910*x^7 + 622*x^8 + 292*x^9 + 74*x^10 + 5*x^11) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 20 2018

A200196 Number of -n..n arrays x(0..6) of 7 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

Original entry on oeis.org

0, 104, 1534, 9856, 40632, 127800, 334278, 765598, 1585416, 3034396, 5450616, 9293800, 15170448, 23863548, 36362438, 53897896, 77976766, 110422568, 153414642, 209534448, 281809258, 373763982, 489469484, 633600106, 811486280
Offset: 1

Views

Author

R. H. Hardin Nov 14 2011

Keywords

Comments

Row 7 of A200192

Examples

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

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)
Showing 1-10 of 10 results.