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 1-6 of 6 results.

A280549 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 9, 50, 144, 325, 670, 1316, 2502, 4654, 8521, 15412, 27612, 49085, 86695, 152282, 266222, 463487, 803970, 1390026, 2396244, 4119894, 7066303, 12093158, 20654128, 35209707, 59919341, 101806274, 172716156, 292607401, 495074182, 836609600
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2017

Keywords

Examples

			Some solutions for n=4:
..0..1..1. .0..1..1. .0..1..1. .0..1..0. .0..1..1. .0..1..0. .0..1..1
..1..0..0. .1..0..0. .1..0..0. .1..0..0. .1..0..1. .1..0..0. .0..0..1
..1..1..0. .0..1..0. .0..1..1. .0..1..0. .1..1..0. .0..1..1. .1..1..0
..1..0..1. .0..1..0. .1..1..0. .0..0..1. .1..0..1. .1..0..1. .0..0..1

Links

Crossrefs

Column 3 of A280554.

Formula

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 10*a(n-4) - 2*a(n-5) - 5*a(n-6) + a(n-7) + a(n-8) for n>10.
Empirical g.f.: x^2*(9 + 5*x - 43*x^2 - 27*x^3 + 63*x^4 + 47*x^5 - 33*x^6 - 25*x^7 + 8*x^8) / ((1 - x)^2*(1 - x - x^2)^3). - Colin Barker, Feb 13 2019

A280550 Number of n X 4 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

1, 34, 144, 382, 832, 1666, 3182, 5886, 10680, 19122, 33920, 59754, 104690, 182598, 317264, 549398, 948528, 1633186, 2805094, 4807006, 8220440, 14030634, 23904656, 40659818, 69051850, 117099910, 198312144, 335420782, 566645728, 956190466
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2017

Keywords

Examples

			Some solutions for n=4:
..0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..1
..0..0..1..0. .1..0..1..1. .1..0..1..0. .1..0..0..1. .1..0..1..1
..1..1..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..1..0..1
..0..1..0..1. .0..1..0..1. .1..0..1..1. .0..1..0..1. .0..0..1..0

Links

Crossrefs

Column 4 of A280554.

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9) for n>11.
Empirical g.f.: x*(1 + 28*x - 48*x^2 - 79*x^3 + 86*x^4 + 142*x^5 - 57*x^6 - 134*x^7 + 46*x^8 + 39*x^9 - 36*x^10) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Feb 13 2019

A280551 Number of n X 5 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 87, 325, 832, 1764, 3438, 6386, 11506, 20389, 35757, 62317, 108150, 187115, 322925, 556071, 955574, 1638882, 2805542, 4794088, 8178068, 13927945, 23683803, 40214243, 68187902, 115469449, 195294823, 329919371, 556731676, 938492304
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2017

Keywords

Examples

			Some solutions for n=4:
..0..1..0..1..0. .0..1..0..1..0. .0..0..1..1..1. .0..1..1..0..1
..1..0..1..0..1. .1..1..0..0..1. .1..1..0..1..0. .1..0..0..1..1
..0..1..1..0..0. .0..1..0..1..0. .0..0..1..0..0. .0..1..1..0..0
..1..0..1..0..1. .1..0..1..0..1. .1..1..0..1..1. .1..0..0..1..0

Links

Crossrefs

Column 5 of A280554.

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9) for n>12.
Empirical g.f.: x*(2 + 75*x - 173*x^2 - 84*x^3 + 213*x^4 + 193*x^5 - 84*x^6 - 209*x^7 + 64*x^8 + 25*x^9 - 76*x^10 + 2*x^11) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Feb 13 2019

A280552 Number of n X 6 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

6, 194, 670, 1666, 3438, 6502, 11697, 20440, 35226, 60300, 102974, 175746, 299975, 512080, 874058, 1491286, 2542606, 4331134, 7369949, 12526488, 21265610, 36058400, 61069118, 103308602, 174569331, 294669456, 496887354, 837059626
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2017

Keywords

Examples

			Some solutions for n=4:
..0..1..0..1..0..1. .0..1..0..1..1..0. .0..1..1..0..0..1. .0..0..1..0..0..0
..1..0..1..0..1..0. .1..0..1..0..1..0. .0..1..0..1..0..1. .1..1..0..1..0..1
..0..1..0..1..0..1. .0..1..0..1..0..1. .1..0..1..0..1..0. .0..0..1..0..1..0
..0..0..1..1..0..1. .1..0..1..1..0..1. .1..0..1..0..1..0. .0..1..0..1..0..1

Links

Crossrefs

Column 6 of A280554.

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9) for n>12.
Empirical g.f.: x*(6 + 158*x - 422*x^2 - 56*x^3 + 440*x^4 + 260*x^5 - 83*x^6 - 314*x^7 + 22*x^8 - 45*x^9 - 142*x^10 + 4*x^11) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Feb 13 2019

A280553 Number of n X 7 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

13, 400, 1316, 3182, 6386, 11697, 20334, 34360, 57389, 95548, 159360, 266756, 448302, 755986, 1278112, 2164458, 3668734, 6220179, 10544150, 17865068, 30247639, 51170104, 86486508, 146040766, 246372038, 415246118, 699240242
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2017

Keywords

Examples

			Some solutions for n=4:
..0..1..1..1..0..1..0. .0..1..0..1..0..1..0. .0..0..1..0..1..1..0
..0..0..1..0..1..0..1. .0..1..0..1..0..1..1. .1..1..0..1..0..0..1
..0..1..0..1..0..1..0. .1..0..1..0..1..0..0. .0..0..1..0..1..1..1
..1..0..1..0..1..0..1. .0..0..0..1..0..1..1. .1..1..0..1..0..0..1

Links

Crossrefs

Column 7 of A280554.

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9) for n>12.
Empirical g.f.: x*(13 + 322*x - 928*x^2 + 21*x^3 + 930*x^4 + 341*x^5 - 79*x^6 - 480*x^7 - 148*x^8 - 205*x^9 - 238*x^10 + 6*x^11) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Feb 13 2019

A280548 Number of n X n 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 0, 50, 382, 1764, 6502, 20334, 56102, 141398, 332810, 743966, 1598198, 3328362, 6763114
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2017

Keywords

Comments

Diagonal of A280554.

Examples

			Some solutions for n=4
..0..1..0..1. .0..1..1..1. .0..1..0..0. .0..1..0..0. .0..0..1..0
..1..1..1..0. .1..0..0..1. .0..1..0..1. .1..0..0..1. .1..1..0..1
..0..1..0..1. .0..1..1..0. .1..0..1..0. .0..1..0..1. .0..0..0..0
..0..0..1..0. .1..0..0..1. .0..0..1..0. .1..0..1..0. .1..1..0..1

Crossrefs

Cf. A280554.
Showing 1-6 of 6 results.

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