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.

A200273 Number of 0..n arrays x(0..5) of 6 elements with zero 3rd differences.

Original entry on oeis.org

2, 3, 6, 9, 14, 25, 36, 47, 64, 87, 110, 143, 176, 209, 258, 311, 364, 431, 498, 575, 666, 761, 856, 969, 1092, 1219, 1364, 1513, 1662, 1847, 2032, 2221, 2432, 2647, 2876, 3135, 3394, 3657, 3946, 4257, 4568, 4913, 5258, 5607, 6004, 6409, 6814, 7257, 7700, 8169
Offset: 1

Views

Author

R. H. Hardin, Nov 15 2011

Keywords

Comments

Row 4 of A200272.

Examples

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

Links

Crossrefs

Cf. A200272.

Formula

Empirical: a(n) = a(n-3) +a(n-5) +a(n-6) -a(n-8) -a(n-9) +a(n-10) -a(n-11) -a(n-13) +a(n-14) -a(n-15) -a(n-16) +a(n-18) +a(n-19) +a(n-21) -a(n-24).
Empirical g.f.: x*(2 + 3*x + 6*x^2 + 7*x^3 + 11*x^4 + 17*x^5 + 22*x^6 + 24*x^7 + 26*x^8 + 33*x^9 + 31*x^10 + 32*x^11 + 26*x^12 + 26*x^13 + 21*x^14 + 15*x^15 + 10*x^16 + 8*x^17 + 6*x^18 + 3*x^19 + 3*x^20 + x^21 - x^23) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x + x^2)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, May 20 2018

A200274 Number of 0..n arrays x(0..6) of 7 elements with zero 4th differences.

Original entry on oeis.org

2, 5, 8, 13, 18, 37, 64, 97, 140, 207, 286, 399, 528, 687, 878, 1127, 1408, 1749, 2130, 2607, 3128, 3743, 4414, 5191, 6056, 7067, 8156, 9387, 10706, 12241, 13876, 15717, 17670, 19829, 22172, 24787, 27542, 30571, 33752, 37317, 41058, 45153, 49440, 54073
Offset: 1

Views

Author

R. H. Hardin, Nov 15 2011

Keywords

Comments

Row 5 of A200272.

Examples

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

Links

Crossrefs

Cf. A200272.

Formula

Empirical: a(n) = a(n-5) +a(n-9) +a(n-10) -a(n-14) -a(n-15) -a(n-19) +a(n-20) +a(n-24) -a(n-25) -a(n-29) -a(n-30) +a(n-34) +a(n-35) +a(n-36) +a(n-39) -a(n-41) -a(n-44) -a(n-45) -a(n-46) +a(n-50) +a(n-51) +a(n-55) -a(n-56) -a(n-60) +a(n-61) +a(n-65) +a(n-66) -a(n-70) -a(n-71) -a(n-75) +a(n-80).

A200275 Number of 0..n arrays x(0..7) of 8 elements with zero 5th differences.

Original entry on oeis.org

2, 5, 8, 13, 26, 53, 112, 197, 302, 465, 688, 1013, 1406, 1995, 2790, 3759, 4990, 6419, 8132, 10281, 13134, 16521, 20352, 24767, 30018, 36095, 43022, 51469, 60976, 71993, 84356, 98137, 113366, 130095, 150630, 173315, 198134, 225225, 254604, 287725
Offset: 1

Views

Author

R. H. Hardin Nov 15 2011

Keywords

Comments

Row 6 of A200272

Examples

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

Links

A200276 Number of 0..n arrays x(0..8) of 9 elements with zero 6th differences.

Original entry on oeis.org

2, 5, 8, 21, 34, 53, 118, 267, 516, 901, 1454, 2249, 3264, 5135, 7616, 11061, 15434, 21089, 28008, 36687, 49294, 65037, 84056, 107327, 134670, 167275, 204986, 256111, 315260, 385087, 464742, 557425, 661956, 781471, 930978, 1102693, 1294980
Offset: 1

Views

Author

R. H. Hardin Nov 15 2011

Keywords

Comments

Row 7 of A200272

Examples

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

Links

A200266 Number of 0..2 arrays x(0..n+1) of n+2 elements with zero n-1st differences.

Original entry on oeis.org

1, 3, 3, 3, 5, 5, 5, 7, 3, 3, 7, 9, 11, 17, 5, 3, 13, 17, 15, 21, 5, 9, 21, 19, 9, 13, 3, 5, 21, 17
Offset: 1

Views

Author

R. H. Hardin Nov 15 2011

Keywords

Comments

Column 2 of A200272

Examples

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

A200267 Number of 0..3 arrays x(0..n+1) of n+2 elements with zero n-1st differences.

Original entry on oeis.org

1, 4, 4, 6, 8, 8, 8, 16, 4, 10, 12, 36, 20, 48, 8, 20, 28, 70, 28, 154, 8, 32, 40, 174, 16, 100, 4, 38, 44, 118
Offset: 1

Views

Author

R. H. Hardin Nov 15 2011

Keywords

Comments

Column 3 of A200272

Examples

			All solutions for n=6
..1....2....2....1....1....3....2....0
..0....3....1....1....2....3....2....0
..1....2....2....1....1....3....2....0
..2....1....3....1....0....3....2....0
..2....1....3....1....0....3....2....0
..1....2....2....1....1....3....2....0
..0....3....1....1....2....3....2....0
..1....2....2....1....1....3....2....0

A200268 Number of 0..4 arrays x(0..n+1) of n+2 elements with zero n-1st differences.

Original entry on oeis.org

1, 5, 7, 9, 13, 13, 21, 31, 19, 37, 75, 139, 97, 181, 101, 225, 277, 505, 465, 971, 225
Offset: 1

Views

Author

R. H. Hardin Nov 15 2011

Keywords

Comments

Column 4 of A200272

Examples

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

A200269 Number of 0..5 arrays x(0..n+1) of n+2 elements with zero n-1st differences.

Original entry on oeis.org

1, 6, 10, 14, 18, 26, 34, 52, 34, 104, 172, 392, 186, 546, 226, 766, 806, 2474, 1202, 4214, 442, 2328
Offset: 1

Views

Author

R. H. Hardin Nov 15 2011

Keywords

Comments

Column 5 of A200272

Examples

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

A200270 Number of 0..6 arrays x(0..n+1) of n+2 elements with zero (n-1)th differences.

Original entry on oeis.org

1, 7, 13, 25, 37, 53, 53, 83, 119, 261, 477, 955, 615, 1617, 937, 2447, 5409, 13829, 9379, 17547
Offset: 1

Views

Author

R. H. Hardin, Nov 15 2011

Keywords

Examples

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

Crossrefs

Column 6 of A200272.

A200271 Number of 0..7 arrays x(0..n+1) of n+2 elements with zero n-1st differences.

Original entry on oeis.org

1, 8, 16, 36, 64, 112, 118, 228, 236, 574, 958, 2110, 1434, 4316, 2560, 8448, 18834, 60888, 38672, 73250, 15518, 42050, 48352, 309524
Offset: 1

Views

Author

R. H. Hardin Nov 15 2011

Keywords

Comments

Column 7 of A200272

Examples

			Some solutions for n=6
..1....2....0....1....0....0....0....0....7....7....7....6....3....2....0....7
..1....4....5....5....6....6....1....3....2....1....2....6....2....7....0....0
..1....2....7....6....5....5....2....5....2....0....2....6....3....7....0....0
..2....0....7....6....3....2....3....6....4....1....3....5....4....5....0....3
..4....0....6....6....3....0....4....6....6....2....3....3....4....3....0....6
..6....2....5....6....5....0....5....5....7....2....2....1....3....2....0....7
..6....4....5....5....6....1....6....3....7....1....2....1....2....2....0....5
..1....2....7....1....0....0....7....0....7....0....7....6....3....2....0....0
Showing 1-10 of 10 results.

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