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 16 results. Next

A199825 Number of -1..1 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

2, 4, 4, 10, 22, 34, 66, 138, 250, 472, 944, 1806, 3450, 6772, 13172, 25478, 49794, 97348, 189772, 371246, 727506, 1424586, 2793034, 5483342, 10766950, 21154424, 41599648, 81840866, 161080918, 317230034, 625030514, 1231964394, 2429323642
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 1 of A199832

Examples

			All solutions for n=3
.-1....0....0....1
.-1....1...-1....1
..0....0....0....0
..1...-1....1...-1
..1....0....0...-1

Links

A199826 Number of -2..2 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

10, 40, 114, 426, 1650, 6126, 23206, 88636, 337866, 1295566, 4992364, 19269156, 74529210, 288954786, 1122363984, 4366362420, 17011617426, 66365823648, 259213619826, 1013542247970, 3966939195402, 15540399135516, 60929935280508
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 2 of A199832

Examples

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

Links

A199827 Number of -3..3 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

24, 140, 646, 3556, 20240, 113884, 645780, 3685550, 21117750, 121503530, 701432670, 4060132070, 23557575574, 136975281374, 797920002262, 4655761528566, 27205829211568, 159187551327960, 932560727269722
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 3 of A199832

Examples

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

Links

A199828 Number of -4..4 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

44, 336, 2146, 15708, 118280, 888420, 6715618, 51077518, 390278378, 2993722414, 23038998514, 177794832922, 1375379617514, 10662124449466, 82808224932874, 644200988262616, 5018935818153796, 39154328577073846, 305823285072243150
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 4 of A199832

Examples

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

Links

A199829 Number of -5..5 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

70, 660, 5390, 49302, 462234, 4340094, 41008804, 389832124, 3723199342, 35697026718, 343371074564, 3312138136660, 32026131818486, 310327172410762, 3012628449222084, 29294846427926718, 285286085845772334
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 5 of A199832

Examples

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

Links

A199830 Number of -6..6 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

102, 1144, 11384, 124982, 1402934, 15805218, 179213048, 2044221894, 23427591518, 269528370904, 3111004900884, 36009192415678, 417810425670462, 4858093196583212, 56593178356427376, 660363780853262084
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 6 of A199832

Examples

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

Links

A199831 Number of -7..7 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

140, 1820, 21364, 273728, 3579520, 47040968, 622300326, 8281149188, 110718596524, 1486040082748, 20010711643976, 270217094416868, 3657780168834780, 49618552941019396, 674346504318284036
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 7 of A199832

Examples

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

Links

A199833 Number of -n..n arrays of 4 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

4, 40, 140, 336, 660, 1144, 1820, 2720, 3876, 5320, 7084, 9200, 11700, 14616, 17980, 21824, 26180, 31080, 36556, 42640, 49364, 56760, 64860, 73696, 83300, 93704, 104940, 117040, 130036, 143960, 158844, 174720, 191620, 209576, 228620, 248784
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Examples

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

Links

Crossrefs

Row 2 of A199832.
Cf. A000447, A016826.

Formula

Empirical: a(n) = (16/3)*n^3 - (4/3)*n = 4*A000447(n).
Empirical: G.f.: 4*x*(1+6*x+x^2) / (x-1)^4 . - R. J. Mathar, Aug 01 2014
Empirical: partial sums of A016826. - Sean A. Irvine, Jul 13 2022

A199834 Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

4, 114, 646, 2146, 5390, 11384, 21364, 36796, 59376, 91030, 133914, 190414, 263146, 354956, 468920, 608344, 776764, 977946, 1215886, 1494810, 1819174, 2193664, 2623196, 3112916, 3668200, 4294654, 4998114, 5784646, 6660546, 7632340, 8706784
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Row 3 of A199832

Examples

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

Links

Formula

Empirical: a(n) = (115/12)*n^4 - (29/6)*n^3 + (5/12)*n^2 - (7/6)*n.
Empirical: G.f.: -2*x*(2+47*x+58*x^2+8*x^3) / (x-1)^5. - R. J. Mathar, Aug 01 2014

A199835 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

10, 426, 3556, 15708, 49302, 124982, 273728, 538968, 978690, 1667554, 2699004, 4187380, 6270030, 9109422, 12895256, 17846576, 24213882, 32281242, 42368404, 54832908, 70072198, 88525734, 110677104, 137056136, 168241010, 204860370
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 4 of A199832

Examples

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

Links

Formula

Empirical: a(n) = n*(2*n+1)*(2*n-1)*(66*n^2-35*n+19)/15.
Empirical: G.f.: 2*x*(5+183*x+575*x^2+281*x^3+12*x^4) / (x-1)^6 . - R. J. Mathar, Aug 01 2014
Showing 1-10 of 16 results. Next

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