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.

A301657 Number of nX3 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 4, 6, 9, 15, 26, 46, 83, 151, 276, 506, 929, 1707, 3138, 5770, 10611, 19515, 35892, 66014, 121417, 223319, 410746, 755478, 1389539, 2555759, 4700772, 8646066, 15902593, 29249427, 53798082, 98950098, 181997603, 334745779, 615693476
Offset: 1

Views

Author

R. H. Hardin, Mar 25 2018

Keywords

Comments

Column 3 of A301662.

Examples

			Some solutions for n=5
..0..0..1. .0..1..0. .0..1..0. .0..1..0. .0..1..0. .0..1..0. .0..1..1
..1..1..0. .1..1..1. .0..1..0. .1..0..1. .1..1..1. .1..0..1. .1..0..0
..0..0..1. .0..1..0. .1..0..1. .1..0..1. .0..1..0. .0..0..0. .0..1..1
..1..1..0. .1..0..1. .1..0..1. .0..1..0. .1..0..1. .1..0..1. .1..0..0
..0..0..1. .0..1..0. .0..1..0. .0..1..0. .1..0..1. .0..1..0. .0..1..1

Links

Crossrefs

Cf. A301662.

Formula

Empirical: a(n) = 2*a(n-1) -a(n-4)

A301658 Number of nX4 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 6, 9, 13, 24, 45, 89, 182, 373, 773, 1604, 3333, 6933, 14422, 30009, 62445, 129944, 270413, 562729, 1171046, 2436965, 5071365, 10553604, 21962245, 45703845, 95110566, 197926889, 411889613, 857150104, 1783745645, 3712008569, 7724760342
Offset: 1

Views

Author

R. H. Hardin, Mar 25 2018

Keywords

Comments

Column 4 of A301662.

Examples

			Some solutions for n=5
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..1..1..0. .1..0..1..0. .1..1..1..0. .1..0..0..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
..1..0..1..0. .1..0..1..0. .1..0..1..0. .1..1..1..0. .1..0..1..0
..0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1

Links

Crossrefs

Cf. A301662.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

A301659 Number of nX5 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 9, 15, 24, 46, 99, 223, 528, 1268, 3085, 7557, 18564, 45712, 112683, 277951, 685904, 1692980, 4179275, 10317757, 25473562, 62893616, 155285391, 383406003, 946650748, 2337341394, 5771057703, 14249158391, 35182226914, 86867560256
Offset: 1

Views

Author

R. H. Hardin, Mar 25 2018

Keywords

Comments

Column 5 of A301662.

Examples

			Some solutions for n=5
..0..1..0..1..0. .0..1..0..1..0. .0..1..0..1..0. .0..1..0..1..0
..0..1..0..1..0. .1..0..1..0..1. .1..0..1..0..1. .1..0..1..0..1
..1..0..1..0..1. .1..0..1..0..1. .0..1..0..1..0. .1..0..1..0..1
..0..1..1..1..0. .0..1..0..1..0. .1..0..1..0..1. .0..1..0..1..0
..1..0..1..0..1. .0..1..0..1..0. .0..1..0..1..0. .1..0..1..0..1

Links

Crossrefs

Cf. A301662.

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) +a(n-3) -4*a(n-4) -4*a(n-6) +3*a(n-7) +3*a(n-8) +a(n-9) +a(n-10) -2*a(n-11)

A301660 Number of nX6 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

13, 14, 26, 45, 99, 254, 696, 2013, 5953, 17878, 54126, 164525, 501455, 1530694, 4676360, 14293737, 43703389, 133647942, 408746766, 1250182369, 3823920719, 11696450282, 35777089740, 109435800649, 334746407201, 1023938030574
Offset: 1

Views

Author

R. H. Hardin, Mar 25 2018

Keywords

Comments

Column 6 of A301662.

Examples

			Some solutions for n=5
..0..1..0..1..0..1. .0..1..0..1..0..1. .0..1..0..1..0..1. .0..1..0..1..0..1
..0..1..0..1..0..1. .1..1..1..0..1..0. .1..0..1..1..1..0. .1..0..1..1..1..0
..1..0..1..0..1..0. .0..1..0..1..0..1. .0..1..0..1..0..1. .0..1..0..1..0..1
..0..1..0..1..1..1. .1..0..0..0..1..0. .1..1..1..0..1..0. .1..0..0..0..1..0
..1..0..1..0..1..0. .0..1..0..1..0..1. .0..1..0..1..0..1. .0..1..0..1..0..1

Links

Crossrefs

Cf. A301662.

Formula

Empirical: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -14*a(n-4) -7*a(n-5) +3*a(n-6) +44*a(n-7) +22*a(n-8) -28*a(n-9) -45*a(n-10) -15*a(n-11) +25*a(n-12) +22*a(n-13) +2*a(n-14) -11*a(n-15) -4*a(n-16) +a(n-17) +2*a(n-18)

A301661 Number of nX7 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

21, 22, 46, 89, 223, 696, 2335, 8380, 31001, 116558, 442314, 1686894, 6453062, 24725894, 94832665, 363935417, 1397133323, 5364622673, 20601302508, 79119265773, 303870780015, 1167097983033, 4482628695760, 17217197273712
Offset: 1

Views

Author

R. H. Hardin, Mar 25 2018

Keywords

Comments

Column 7 of A301662.

Examples

			Some solutions for n=5
..0..1..0..1..0..1..0. .0..1..0..1..0..1..1. .0..1..0..0..1..0..1
..1..0..1..0..0..0..1. .1..0..1..1..1..0..0. .1..0..1..1..0..1..0
..0..0..0..1..0..1..0. .0..1..0..1..0..1..1. .0..1..0..0..1..1..1
..1..0..1..0..1..0..1. .1..1..1..0..1..0..0. .1..0..1..1..0..1..0
..0..1..0..1..0..1..0. .0..1..0..1..0..1..1. .0..1..0..0..1..0..1

Links

Crossrefs

Cf. A301662.

Formula

Empirical: a(n) = 5*a(n-1) -5*a(n-2) +14*a(n-3) -44*a(n-4) -2*a(n-5) -63*a(n-6) +117*a(n-7) +133*a(n-8) +386*a(n-9) +126*a(n-10) -575*a(n-11) -1064*a(n-12) -876*a(n-13) +203*a(n-14) +1305*a(n-15) +1617*a(n-16) +681*a(n-17) -882*a(n-18) -1502*a(n-19) -879*a(n-20) +297*a(n-21) +793*a(n-22) +486*a(n-23) +6*a(n-24) -191*a(n-25) -108*a(n-26) -14*a(n-27) +20*a(n-28) +12*a(n-29) +4*a(n-30) +a(n-31)

A301656 Number of n X n 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 3, 6, 13, 46, 254, 2335, 37679, 1036686, 47847128, 3666918138, 462476814296, 95511722707577, 32204769674856063, 17694312704564808047, 15825068959028242214319
Offset: 1

Views

Author

R. H. Hardin, Mar 25 2018

Keywords

Comments

Diagonal of A301662.

Examples

			Some solutions for n=5
..0..1..0..1..0. .0..1..0..1..0. .0..1..0..1..0. .0..1..0..1..0
..1..0..0..0..1. .1..0..1..1..1. .1..0..1..0..1. .0..1..0..1..0
..0..1..0..1..0. .0..1..0..1..0. .0..1..1..1..0. .1..0..1..0..1
..1..0..1..0..1. .1..0..1..0..1. .1..0..1..0..1. .0..1..0..1..0
..1..0..1..0..1. .1..0..1..0..1. .0..1..0..1..0. .1..0..1..0..1

Crossrefs

Cf. A301662.
Showing 1-6 of 6 results.

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