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 12 results. Next

A249975 Number of length n+1 0..2*1 arrays with the sum of the absolute values of adjacent differences equal to n*1.

Original entry on oeis.org

4, 10, 20, 64, 136, 466, 1012, 3580, 7864, 28340, 62696, 228700, 508400, 1870466, 4172660, 15449740, 34557400, 128583340, 288212440, 1076603824, 2417218544, 9058241620, 20366034760, 76521687304, 172247070064, 648634854904
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Column 1 of A249982

Examples

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

Links

A249976 Number of length n+1 0..2*2 arrays with the sum of the absolute values of adjacent differences equal to n*2.

Original entry on oeis.org

6, 24, 88, 384, 1606, 7138, 31380, 141272, 635686, 2890884, 13175784, 60384934, 277442652, 1279055676, 5909701748, 27368939688, 126981852654, 590182327132, 2747109920736, 12804571294224, 59756343262648, 279183944932752
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Column 2 of A249982

Examples

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

Links

A249977 Number of length n+1 0..2*3 arrays with the sum of the absolute values of adjacent differences equal to n*3.

Original entry on oeis.org

8, 42, 208, 1242, 6856, 43068, 245860, 1589346, 9213728, 60568000, 354452340, 2354520904, 13870730416, 92791873776, 549357227852, 3693928360378, 21952690573088, 148190103229340, 883335481978896, 5981390826179620
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Column 3 of A249982

Examples

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

Links

A249978 Number of length n+1 0..2 X 4 arrays with the sum of the absolute values of adjacent differences equal to n*4.

Original entry on oeis.org

10, 64, 426, 3030, 22560, 168506, 1293326, 9937894, 77372824, 604180880, 4749038012, 37448196486, 296429721556, 2352824897458, 18723425845436, 149319341015310, 1193131013642304, 9549922015472032, 76554889282313192
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Column 4 of A249982

Examples

			Some solutions for n=6
..4....0....1....0....0....0....3....2....0....2....1....2....1....3....2....1
..1....2....8....7....7....3....8....8....4....0....1....8....3....0....8....6
..5....3....6....6....0....3....2....4....3....8....6....3....6....6....0....1
..3....8....7....3....0....8....0....2....0....0....3....1....1....0....3....6
..8....2....6....7....4....5....8....0....7....3....0....2....0....7....7....1
..2....8....0....8....8....0....8....6....3....3....7....0....8....6....5....4
..6....4....7....0....6....8....5....2....8....0....1....8....3....5....6....3

Links

A249979 Number of length n+1 0..2*5 arrays with the sum of the absolute values of adjacent differences equal to n*5.

Original entry on oeis.org

12, 90, 728, 6252, 55372, 508902, 4598532, 43752328, 399919272, 3872197278, 35715136808, 349291390860, 3244120777620, 31938382591862, 298193263675024, 2949970866347064, 27653133418970008, 274591500744039956
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Column 5 of A249982

Examples

			Some solutions for n=5
..4....7....3....8...10....8....7....4....7....8....0....4....8....5....7....9
..9....3....6...10....3....5...10....3....0....3....1....7....2....2....2....3
..2....7....3....2....4...10....7....1....7....9....9....3....6....9...10...10
..9....9....0....8...10....3....1...10....4....2....9....0....0....3....2....1
..4....0....9....1....3....9....8....3....9....5....1...10....1....6....1....2
..5....6....2....3....7....5....2....9....6....1....9....5....9....0....4....0

Links

A249980 Number of length n+1 0..2*6 arrays with the sum of the absolute values of adjacent differences equal to n*6.

Original entry on oeis.org

14, 120, 1178, 11524, 123154, 1290856, 14027522, 152155572, 1672105528, 18444783546, 204618309890, 2278761969748, 25463763359360, 285391177688962, 3206446229163896, 36105694885521924, 407337937707100144
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Column 6 of A249982.

Examples

			Some solutions for n=5
..4....1....1....2....9...11....4....0...11....3....3....8....0....6...10....9
..2....5....0...11....5....0....2....2....1....6....3....6....9...12....8....5
.11...10....4....8...11....3....6...12....3....1....0....1....1....5...12....0
..2...12...11....3....1....9....9....2...11...12...10...12....5....5....3....1
..8....1....2...11....2....1....0....6....8....6....0....3....2...12...11...11
..4....9...11....6...11....3...12....2....1....1....7....6....8....2....4....1

Links

Crossrefs

Cf. A249982.

A249981 Number of length n+1 0..2*7 arrays with the sum of the absolute values of adjacent differences equal to n*7.

Original entry on oeis.org

16, 154, 1744, 19574, 237348, 2886016, 35380112, 446342246, 5529256528, 70948896558, 887325882364, 11494042429460, 144804789146232, 1887744535279984, 23911022925991996, 313197804513008262
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Column 7 of A249982

Examples

			Some solutions for n=4
..8....6...11....2....6....6....7....4...14...11....2....1....6...12....8...12
..2...10....5...13...13...10....2...13....2....2....0....9....8....8....5....9
..9....6...14...10....3....1...14....4....0....0...13...14....5....2....9...11
..4....0....8...14....2...11...13....8....2...14...14....3...14...10....0....0
.14...14....1....4...12....6....3....2...14...11....2....7....0....0...12...12

Links

A249983 Number of length 3+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 3*n.

Original entry on oeis.org

20, 88, 208, 426, 728, 1178, 1744, 2508, 3420, 4580, 5920, 7558, 9408, 11606, 14048, 16888, 20004, 23568, 27440, 31810, 36520, 41778, 47408, 53636, 60268, 67548, 75264, 83678, 92560, 102190, 112320, 123248, 134708, 147016, 159888, 173658, 188024
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Examples

			Some solutions for n=6:
..9...11....5...12....2....4....5...11....4....7....0....0...11....8...12....4
..1....1...11....4....0...11....0...10....2....0....8....1....1...12....4...12
..2....4....2...10...10....6...10....2...10....1...10...10....0....0....3....7
.11....9....5....6....4....0....7...11....2...11....2....2....7....2...12...12

Links

Crossrefs

Row 3 of A249982.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
Empirical for n mod 2 = 0: a(n) = (41/12)*n^3 + (43/4)*n^2 + (53/6)*n.
Empirical for n mod 2 = 1: a(n) = (41/12)*n^3 + (43/4)*n^2 + (79/12)*n - (3/4).
Empirical g.f.: 2*x*(10 + 24*x + 6*x^2 + x^3) / ((1 - x)^4*(1 + x)^2). - Colin Barker, Nov 10 2018

A249984 Number of length 4+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 4*n.

Original entry on oeis.org

64, 384, 1242, 3030, 6252, 11524, 19574, 31242, 47480, 69352, 98034, 134814, 181092, 238380, 308302, 392594, 493104, 611792, 750730, 912102, 1098204, 1311444, 1554342, 1829530, 2139752, 2487864, 2876834, 3309742, 3789780, 4320252, 4904574
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Examples

			Some solutions for n=6:
..3...12....2....1....6....9...12....2....8...12....3....2...11...12....2....2
..0....0....9...11....2....3....2...11....0....6...11....6...12....1...12....9
.12....6....1....8...10....8...10....9....9...11....0...12....0....7....3....1
.10....6....1....0....5....2....6...11....3....0....1....5....4....2....7....3
..3....0...10....3...12....9....8....0....4....2....5...12...11....0....6...10

Links

Crossrefs

Row 4 of A249982.

Formula

Empirical: a(n) = (14/3)*n^4 + (56/3)*n^3 + (121/3)*n^2 - (5/3)*n + 2.
Conjectures from Colin Barker, Nov 10 2018: (Start)
G.f.: 2*x*(32 + 32*x - 19*x^2 + 10*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A249985 Number of length 5+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 5*n.

Original entry on oeis.org

136, 1606, 6856, 22560, 55372, 123154, 237348, 434042, 728724, 1184066, 1817540, 2728080, 3931760, 5574774, 7667096, 10414498, 13814832, 18147086, 23389648, 29909680, 37657444, 47104554, 58163164, 71426938, 86758620, 104892842
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Examples

			Some solutions for n=6:
.10....7....1....1....2....8....2....0....0....2....3....3...11....1...11....8
..0...10....6....6....8....0....6....4...12....9....4....0....2....9....1....3
..1...11....7....9....0...11...10....7....6....1...11...12....3....8....5...11
.10....1....0....1....9....7....0...12....6...12....8....4...11....4....0....3
..8....9....9...10....4....1...10....3...10...11....0....2....1...12....7....1
..0....1....1....5....6....2...12...12....2....8...11....7....3....3...11....8

Links

Crossrefs

Row 5 of A249982.

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).
Empirical for n mod 2 = 0: a(n) = (1739/240)*n^5 + (3679/96)*n^4 + (859/12)*n^3 + (1121/24)*n^2 - (4/15)*n + 2.
Empirical for n mod 2 = 1: a(n) = (1739/240)*n^5 + (3679/96)*n^4 + (1553/24)*n^3 + (1357/48)*n^2 - (949/240)*n + (45/32).
Empirical g.f.: 2*x*(68 + 667*x + 1618*x^2 + 2559*x^3 + 1402*x^4 + 579*x^5 + 58*x^6 + 4*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4) - Colin Barker, Nov 10 2018.
Showing 1-10 of 12 results. Next

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