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 13 results. Next

A200546 Number of -1..1 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

Original entry on oeis.org

4, 14, 26, 72, 142, 362, 778, 1938, 4366, 10628, 24532, 59138, 138680, 333014, 788374, 1890870, 4503208, 10803262, 25831504, 62025512, 148725902, 357516682, 859055042, 2067463940, 4975921904, 11988835382, 28892947100, 69685951942
Offset: 1

Views

Author

R. H. Hardin Nov 19 2011

Keywords

Comments

Column 1 of A200553

Examples

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

Links

A200547 Number of -2..2 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

Original entry on oeis.org

14, 76, 280, 1240, 4978, 21626, 91058, 393660, 1686980, 7309386, 31632968, 137600876, 599055566, 2615427970, 11433493630, 50075195034, 219589525108, 964264276780, 4238966033150, 18655002576606, 82175337524524, 362306822490256, 1598684706408864, 7059561038745824
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2011

Keywords

Examples

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

Links

Crossrefs

Column 2 of A200553.

A200548 Number of -3..3 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

Original entry on oeis.org

30, 200, 1184, 7254, 43698, 266812, 1639804, 10152636, 63132188, 394016210, 2466471522, 15481097890, 97396742734, 614019893832, 3878005568152, 24532092598782, 155413031752230, 985836563404470, 6260856742508844
Offset: 1

Views

Author

R. H. Hardin Nov 19 2011

Keywords

Comments

Column 3 of A200553

Examples

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

Links

A200549 Number of -4..4 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

Original entry on oeis.org

52, 446, 3396, 26850, 211374, 1689732, 13587804, 109957140, 893510530, 7288331916, 59637096784, 489325754576, 4024444316206, 33167657580268, 273853057747366, 2264784856966600, 18757225819498566, 155553439876468586
Offset: 1

Views

Author

R. H. Hardin Nov 19 2011

Keywords

Comments

Column 4 of A200553

Examples

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

Links

A200550 Number of -5..5 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

Original entry on oeis.org

80, 836, 7778, 75792, 737460, 7286542, 72366820, 723237026, 7258296910, 73127883596, 739101010202, 7490787201124, 76099633989974, 774719436417776, 7901415122713726, 80719023935569240, 825814487838111514
Offset: 1

Views

Author

R. H. Hardin Nov 19 2011

Keywords

Comments

Column 5 of A200553

Examples

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

Links

A200551 Number of -6..6 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

Original entry on oeis.org

114, 1368, 15476, 178834, 2076774, 24378976, 288237528, 3427837106, 40950125796, 491063998130, 5907663402532, 71267752107030, 861806880210532, 10443265297671942, 126784115884242080, 1541722886174306634
Offset: 1

Views

Author

R. H. Hardin Nov 19 2011

Keywords

Comments

Column 6 of A200553

Examples

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

Links

A200552 Number of -7..7 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

Original entry on oeis.org

154, 2134, 27806, 372150, 5012084, 68263780, 936121220, 12911643944, 178893425570, 2488110363432, 34717386812304, 485767803378730, 6813227225653584, 95761068651953630, 1348433104134460586
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2011

Keywords

Comments

Column 7 of A200553.

Examples

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

Links

Crossrefs

Cf. A200553.

A200554 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second differences.

Original entry on oeis.org

14, 76, 200, 446, 836, 1368, 2134, 3140, 4368, 5942, 7852, 10064, 12734, 15836, 19320, 23374, 27956, 33000, 38726, 45076, 51968, 59654, 68060, 77088, 87022, 97772, 109224, 121694, 135076, 149240, 164534, 180836, 198000, 216406, 235916, 256368, 278174, 301180, 325208
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2011

Keywords

Examples

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

Links

Crossrefs

Row 2 of A200553.

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8).
Empirical g.f.: 2*x*(7 + 24*x + 31*x^2 + 47*x^3 + 24*x^4 + 9*x^5 + 2*x^6) / ((1 - x)^4*(1 + x + x^2)^2). - Colin Barker, May 21 2018

A200555 Number of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero second differences.

Original entry on oeis.org

26, 280, 1184, 3396, 7778, 15476, 27806, 46346, 72902, 109528, 158422, 222162, 303412, 405134, 530518, 683014, 866156, 1083954, 1340420, 1639900, 1986968, 2386470, 2843276, 3362828, 3950486, 4611980, 5353268, 6180592, 7100158, 8118840
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2011

Keywords

Comments

Row 3 of A200553.

Examples

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

Links

Crossrefs

Cf. A200553.

Formula

Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-4) -3*a(n-5) +3*a(n-6) +3*a(n-7) -2*a(n-9) -a(n-10) +a(n-11).
Empirical g.f.: 2*x*(13 + 127*x + 426*x^2 + 826*x^3 + 1046*x^4 + 912*x^5 + 544*x^6 + 205*x^7 + 37*x^8 + 4*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)^2). - Colin Barker, May 21 2018

A200556 Number of -n..n arrays x(0..5) of 6 elements with zero sum and nonzero second differences.

Original entry on oeis.org

72, 1240, 7254, 26850, 75792, 178834, 372150, 705270, 1242888, 2067650, 3281874, 5009232, 7397868, 10621792, 14882672, 20413220, 27478160, 36376230, 47443518, 61054528, 77624122, 97610834, 121518006, 149895400, 183343046, 222512226
Offset: 1

Views

Author

R. H. Hardin Nov 19 2011

Keywords

Comments

Row 4 of A200553

Examples

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

Links

Formula

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -2*a(n-4) -a(n-6) -a(n-7) -a(n-8) +3*a(n-9) +3*a(n-10) -a(n-11) -a(n-12) -a(n-13) -2*a(n-15) +a(n-16) +a(n-17) +a(n-18) -a(n-19)
Showing 1-10 of 13 results. Next

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