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 11 results. Next

A297390 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

3, 9, 19, 57, 139, 369, 963, 2489, 6523, 16929, 44147, 114953, 299307, 779697, 2030243, 5287833, 13770971, 35864001, 93402579, 243249193, 633503627, 1649849553, 4296752131, 11190160825, 29142853947, 75897603297, 197662332211
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Examples

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

Crossrefs

Column 3 of A297395.

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 2*a(n-3) - 4*a(n-4).
Empirical g.f.: x*(1 + 2*x)*(3 - 2*x^2) / (1 - x - 4*x^2 - 2*x^3 + 4*x^4). - Colin Barker, Feb 28 2019

A297391 Number of n X 4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

4, 13, 37, 126, 385, 1243, 3924, 12477, 39625, 125780, 399527, 1268481, 4028320, 12791471, 40619227, 128985178, 409588149, 1300636903, 4130132236, 13115120227, 41646681705, 132247843570, 419949219621, 1333536652989, 4234607278278
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Examples

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

Crossrefs

Column 4 of A297395.

Formula

Empirical: a(n) = a(n-1) + 6*a(n-2) + 4*a(n-3) - 3*a(n-4) - a(n-5) - 2*a(n-6) - a(n-7).
Empirical g.f.: x*(4 + 9*x - 5*x^3 - 3*x^4 - 3*x^5 - x^6) / (1 - x - 6*x^2 - 4*x^3 + 3*x^4 + x^5 + 2*x^6 + x^7). - Colin Barker, Feb 28 2019

A297392 Number of nX5 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

6, 33, 127, 700, 3175, 15541, 74736, 358341, 1729617, 8308924, 40006463, 192481249, 926168176, 4456879585, 21445119255, 103193473908, 496552428929, 2389355832929, 11497320733428, 55323763675221, 266211857683333
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Comments

Column 5 of A297395.

Examples

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

Crossrefs

Cf. A297395.

Formula

Empirical: a(n) = a(n-1) +8*a(n-2) +27*a(n-3) +77*a(n-4) +164*a(n-5) -4*a(n-6) -124*a(n-7) -71*a(n-8) -231*a(n-9) -293*a(n-10) -114*a(n-11) -16*a(n-12) +2*a(n-13) +40*a(n-14) +98*a(n-15) +32*a(n-16) +16*a(n-17) +5*a(n-18) +a(n-19) -a(n-20)

A297393 Number of nX6 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

9, 69, 323, 2569, 14940, 99682, 640562, 4101278, 26607999, 170810312, 1102871801, 7104859427, 45791052572, 295185451556, 1902301744507, 12261796238309, 79028574384941, 509365351856610, 3283017190154762, 21159928491044181
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Comments

Column 6 of A297395.

Examples

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

Crossrefs

Cf. A297395.

Formula

Empirical: a(n) = 2*a(n-1) +16*a(n-2) +55*a(n-3) +143*a(n-4) +377*a(n-5) -1022*a(n-6) -1350*a(n-7) -647*a(n-8) -3863*a(n-9) -4798*a(n-10) -4588*a(n-11) +36964*a(n-12) +21604*a(n-13) +14553*a(n-14) +107577*a(n-15) +51945*a(n-16) -52831*a(n-17) -345125*a(n-18) -312451*a(n-19) -218764*a(n-20) -24650*a(n-21) +55508*a(n-22) +98904*a(n-23) +3168*a(n-24) -16128*a(n-25)

A297394 Number of nX7 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

13, 121, 763, 7779, 58901, 514945, 4279111, 35870939, 302197213, 2529537475, 21265881307, 178394566329, 1497728421519, 12572164720815, 105527179560835, 885843035970095, 7435701167074899, 62416764116955877, 523932061650568927
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Comments

Column 7 of A297395.

Examples

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

Crossrefs

Cf. A297395.

Formula

Empirical: a(n) = 3*a(n-1) +21*a(n-2) +113*a(n-3) +610*a(n-4) +1954*a(n-5) -4513*a(n-6) -7036*a(n-7) -16044*a(n-8) -37255*a(n-9) -189191*a(n-10) -101505*a(n-11) +1077305*a(n-12) -76893*a(n-13) +4362207*a(n-14) +4958045*a(n-15) +3944814*a(n-16) -11934716*a(n-17) -39264119*a(n-18) +45663237*a(n-19) -362097902*a(n-20) +144009367*a(n-21) +200365107*a(n-22) +280079512*a(n-23) -59590023*a(n-24) +600520779*a(n-25) -1164824474*a(n-26) +98532137*a(n-27) +197933528*a(n-28) +368130672*a(n-29) -355078850*a(n-30) +500273702*a(n-31) -601298054*a(n-32) +159089952*a(n-33) -77802073*a(n-34) -69297690*a(n-35) +140314988*a(n-36) +43541186*a(n-37) -27225972*a(n-38) +12272424*a(n-39) -4707802*a(n-40) -36757204*a(n-41) +13875238*a(n-42) +13080780*a(n-43) -1686728*a(n-44) -2007356*a(n-45) -1024492*a(n-46) -820088*a(n-47) +472256*a(n-48) +86872*a(n-49) +46204*a(n-50) -19264*a(n-51) +5704*a(n-52) +480*a(n-53) -192*a(n-54) +24*a(n-55)

A297396 Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

1, 9, 19, 37, 127, 323, 763, 2121, 5557, 14031, 37065, 97027, 250371, 653707, 1706245, 4431885, 11544027, 30085525, 78290135, 203852347, 530958219, 1382353401, 3599332477, 9373032927, 24405570561, 63547912011, 165475162027, 430875964651
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Examples

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

Crossrefs

Row 3 of A297395.

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 8*a(n-3) + a(n-4) - 2*a(n-6).
Empirical g.f.: x*(1 + 8*x + 9*x^2 + x^3 - 2*x^4 - 2*x^5) / (1 - x - x^2 - 8*x^3 - x^4 + 2*x^6). - Colin Barker, Feb 28 2019

A297397 Number of 4 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

1, 20, 57, 126, 700, 2569, 7779, 31081, 117084, 400727, 1478944, 5485580, 19599269, 71231855, 261062287, 945122754, 3430304343, 12504256178, 45424857782, 164983194009, 600231458537, 2182009835511, 7929300624520, 28830589829675
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Examples

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

Crossrefs

Row 4 of A297395.

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) + 24*a(n-3) + 11*a(n-4) - 21*a(n-5) - 67*a(n-6) - 9*a(n-7) - 45*a(n-8).
Empirical g.f.: x*(1 + 19*x + 34*x^2 - 15*x^3 - 88*x^4 - 76*x^5 - 54*x^6 - 45*x^7) / (1 - x - 3*x^2 - 24*x^3 - 11*x^4 + 21*x^5 + 67*x^6 + 9*x^7 + 45*x^8). - Colin Barker, Feb 28 2019

A297398 Number of 5Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

1, 41, 139, 385, 3175, 14940, 58901, 325922, 1616869, 7303419, 36440971, 179690470, 852213260, 4150469302, 20279868193, 97720833639, 473767953000, 2303837003374, 11153405540217, 54053378441391, 262342164214663, 1271623035196752
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Comments

Row 5 of A297395.

Examples

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

Crossrefs

Cf. A297395.

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +69*a(n-3) +50*a(n-4) -a(n-5) -785*a(n-6) -696*a(n-7) -757*a(n-8) +2847*a(n-9) +1739*a(n-10) +270*a(n-11) -1916*a(n-12) -1560*a(n-13) -932*a(n-14) +1326*a(n-15) +652*a(n-16) +140*a(n-17) -373*a(n-18) -14*a(n-19) -28*a(n-20) +30*a(n-21)

A297399 Number of 6Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

1, 85, 369, 1243, 15541, 99682, 514945, 3977868, 27131403, 165041224, 1128035711, 7625285858, 49170022362, 326850563103, 2183716617103, 14348810814654, 94917649585924, 630373096158959, 4164712261202289, 27543277723412233
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Comments

Row 6 of A297395.

Examples

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

Crossrefs

Cf. A297395.

Formula

Empirical: a(n) = a(n-1) +6*a(n-2) +210*a(n-3) +229*a(n-4) +55*a(n-5) -9886*a(n-6) -14173*a(n-7) -8075*a(n-8) +195748*a(n-9) +181875*a(n-10) +87663*a(n-11) -1422344*a(n-12) -337739*a(n-13) -1114957*a(n-14) +5525820*a(n-15) -2908803*a(n-16) -871445*a(n-17) -12476178*a(n-18) +150124*a(n-19) +5056777*a(n-20) +2216204*a(n-21) -5969575*a(n-22) -10404139*a(n-23) +965484*a(n-24) +7909580*a(n-25) +142084*a(n-26) -4532588*a(n-27) -259328*a(n-28) +1045248*a(n-29) +23360*a(n-30) -64512*a(n-31)

A297400 Number of 7Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

1, 178, 963, 3924, 74736, 640562, 4279111, 46261441, 428200086, 3465586864, 32328050104, 296748190460, 2574529121380, 23200388627087, 210159449303417, 1865437561436124, 16702908801335717, 150242351184841826
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2017

Keywords

Comments

Row 7 of A297395.

Examples

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

Crossrefs

Cf. A297395.

Formula

Empirical recurrence of order 69 (see link above)
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