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.

A200083 Number of 0..n arrays x(0..4) of 5 elements with zero 3rd differences.

Original entry on oeis.org

2, 3, 8, 17, 26, 43, 64, 89, 122, 163, 208, 269, 334, 407, 496, 597, 702, 831, 968, 1117, 1286, 1471, 1664, 1889, 2122, 2371, 2648, 2945, 3250, 3595, 3952, 4329, 4738, 5171, 5616, 6109, 6614, 7143, 7712, 8309, 8918, 9583, 10264, 10973, 11726, 12511, 13312
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2011

Keywords

Comments

Row 4 of A200082.

Examples

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

Links

Crossrefs

Cf. A200082.

Formula

Empirical: a(n) = a(n-1) +a(n-3) -a(n-5) +a(n-6) -2*a(n-7) +a(n-8) -a(n-9) +a(n-11) +a(n-13) -a(n-14).
Empirical g.f.: x*(2 + x + 5*x^2 + 7*x^3 + 6*x^4 + 11*x^5 + 5*x^6 + 8*x^7 + 3*x^8 + x^9 + 2*x^10 + x^11 + x^12 - x^13) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, May 17 2018

A200084 Number of 0..n arrays x(0..5) of 6 elements with zero 4th differences.

Original entry on oeis.org

2, 7, 14, 27, 58, 111, 182, 279, 404, 617, 872, 1199, 1580, 2045, 2678, 3437, 4300, 5305, 6430, 7903, 9530, 11389, 13420, 15707, 18460, 21537, 24870, 28553, 32518, 37265, 42342, 47905, 53828, 60267, 67620, 75589, 84034, 93127, 102734, 113729, 125300
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2011

Keywords

Comments

Row 5 of A200082.

Examples

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

Links

Crossrefs

Cf. A200082.

Formula

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +2*a(n-10) -2*a(n-11) -2*a(n-12) +2*a(n-13) +a(n-15) -a(n-16) -a(n-17) +a(n-18) -a(n-20) +a(n-21) +a(n-22) -a(n-23) -2*a(n-25) +2*a(n-26) +2*a(n-27) -2*a(n-28) +a(n-35) -a(n-36) -a(n-37) +a(n-38).

A200085 Number of 0..n arrays x(0..6) of 7 elements with zero 5th differences.

Original entry on oeis.org

2, 9, 18, 37, 108, 245, 454, 759, 1172, 2001, 3144, 4663, 6568, 8945, 12690, 17353, 23022, 29787, 37710, 48921, 62130, 77465, 95100, 115177, 141596, 171767, 205850, 244065, 286652, 340277, 400038, 466375, 539488, 619685, 717388, 824733, 942014
Offset: 1

Views

Author

R. H. Hardin Nov 13 2011

Keywords

Comments

Row 6 of A200082

Examples

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

Links

Formula

Empirical: a(n) = a(n-1) +a(n-5) -a(n-7) +a(n-10) -2*a(n-11) +a(n-12) -a(n-16) +a(n-17) -a(n-20) +a(n-21) -a(n-25) +2*a(n-26) -a(n-27) +a(n-30) -a(n-32) -a(n-36) +a(n-37) +a(n-45) -a(n-46) -a(n-50) +a(n-52) -a(n-55) +2*a(n-56) -a(n-57) +a(n-61) -a(n-62) +a(n-65) -a(n-66) +a(n-70) -2*a(n-71) +a(n-72) -a(n-75) +a(n-77) +a(n-81) -a(n-82)

A200086 Number of 0..n arrays x(0..7) of 8 elements with zero 6th differences.

Original entry on oeis.org

2, 9, 24, 85, 202, 429, 1046, 2145, 4022, 6955, 11438, 17927, 26868, 41817, 62238, 89715, 125864, 172459, 231700, 305753, 409430, 537577, 695264, 886875, 1116878, 1391945, 1717032, 2134089, 2625830, 3201035, 3869292, 4642295, 5530982, 6546651
Offset: 1

Views

Author

R. H. Hardin Nov 13 2011

Keywords

Comments

Row 7 of A200082

Examples

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

Links

A200076 Number of 0..2 arrays x(0..n) of n+1 elements with zero n-1st differences.

Original entry on oeis.org

1, 3, 3, 3, 7, 9, 9, 15, 7, 3, 11, 29, 43, 73, 25, 5, 27, 53, 97, 123, 29, 41, 93, 85, 35, 35, 17, 9, 55, 73
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2011

Keywords

Comments

Column 2 of A200082.

Examples

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

Crossrefs

Cf. A200082.

A200077 Number of 0..3 arrays x(0..n) of n+1 elements with zero n-1st differences.

Original entry on oeis.org

1, 4, 6, 8, 14, 18, 24, 56, 26, 26, 54, 226, 260, 482, 196, 54, 128, 728, 1226, 4106, 1168, 272, 892, 4798, 1390, 1298, 962, 216, 470, 2104
Offset: 1

Views

Author

R. H. Hardin Nov 13 2011

Keywords

Comments

Column 3 of A200082

Examples

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

A200078 Number of 0..4 arrays x(0..n) of n+1 elements with zero n-1st differences.

Original entry on oeis.org

1, 5, 9, 17, 27, 37, 85, 169, 151, 219, 533, 1553, 2333, 4197, 2607, 2419, 6343, 25235, 55337, 113875, 35671
Offset: 1

Views

Author

R. H. Hardin Nov 13 2011

Keywords

Comments

Column 4 of A200082

Examples

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

A200079 Number of 0..5 arrays x(0..n) of n+1 elements with zero n-1st differences.

Original entry on oeis.org

1, 6, 12, 26, 58, 108, 202, 394, 468, 848, 2560, 7740, 11372, 28356, 20660, 20032, 68026, 312678, 662542, 1536878, 812306, 461910, 1466416, 10325202
Offset: 1

Views

Author

R. H. Hardin Nov 13 2011

Keywords

Comments

Column 5 of A200082

Examples

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

A200080 Number of 0..6 arrays x(0..n) of n+1 elements with zero n-1st differences.

Original entry on oeis.org

1, 7, 17, 43, 111, 245, 429, 855, 1863, 3573, 10241, 30645, 50043, 160499, 149009, 149121, 755895, 3366835
Offset: 1

Views

Author

R. H. Hardin Nov 13 2011

Keywords

Comments

Column 6 of A200082

Examples

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

A200081 Number of 0..7 arrays x(0..n) of n+1 elements with zero n-1st differences.

Original entry on oeis.org

1, 8, 22, 64, 182, 454, 1046, 2546, 5056, 11638, 33262, 101112, 191802, 688304, 769106, 1102184, 5220960, 23546744, 49886556, 135889790, 142614238, 121124812, 570957758
Offset: 1

Views

Author

R. H. Hardin Nov 13 2011

Keywords

Comments

Column 7 of A200082

Examples

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

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