A302163 -id:A302163 - cp's OEIS frontend

A302164 Number of 2Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

2, 3, 9, 17, 25, 65, 185, 385, 649, 1489, 3929, 8609, 15913, 34545, 85497, 191809, 377545, 802961, 1894553, 4279521, 8785769, 18612785, 42501945, 95817857, 202153993, 429672401, 960801241, 2153871393, 4621792425, 9879318897

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Row 2 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6

A302157 Number of n X n 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 3, 7, 29, 140, 635, 2853, 19993, 75825, 786161, 2915241, 49663915, 152854596, 4893607560, 13149908952, 764803558904, 1748158857032, 193883417013099, 378301363005384, 78801036106269590, 130887347815375440

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Diagonal of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..22

Cf. A302163.

A302158 Number of nX3 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 9, 7, 17, 31, 57, 111, 265, 527, 1065, 2431, 4953, 10095, 22537, 46527, 95417, 209679, 436585, 900191, 1955353, 4093999, 8480457, 18265087, 38377337, 79802575, 170819881, 359693471, 750304217, 1598909295, 3371088777, 7049660735

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Column 3 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +8*a(n-3) -6*a(n-4) -4*a(n-6) +4*a(n-7) for n>11

A302159 Number of nX4 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 17, 12, 29, 73, 156, 361, 865, 1970, 4530, 10571, 24394, 56204, 130230, 301221, 695541, 1608549, 3720177, 8597848, 19876759, 45959426, 106246321, 245619039, 567865144, 1312830532, 3035049693, 7016724012, 16221856134, 37502724170

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Column 4 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +a(n-2) +6*a(n-3) -4*a(n-5) -7*a(n-6) -a(n-7) +3*a(n-8) +2*a(n-9) -a(n-10) -4*a(n-11) -3*a(n-12) +a(n-13) +2*a(n-14) +2*a(n-15) for n>19

A302160 Number of nX5 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 25, 20, 51, 140, 280, 621, 1451, 3189, 7136, 16179, 36212, 81254, 182957, 410889, 922943, 2074950, 4662563, 10476618, 23545560, 52912545, 118903861, 267210837, 600490496, 1349441183, 3032538210, 6814874446, 15314690189, 34415928927

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Column 5 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +a(n-2) +7*a(n-3) -3*a(n-4) -3*a(n-5) -14*a(n-6) +3*a(n-7) +2*a(n-8) +9*a(n-9) -2*a(n-10) -2*a(n-12) for n>15

A302161 Number of nX6 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

13, 65, 34, 109, 296, 635, 1563, 3948, 9405, 22602, 55730, 135448, 327429, 798275, 1944498, 4720205, 11478126, 27935558, 67913732, 165112453, 401615997, 976675958, 2374829337, 5775344378, 14045080684, 34154018024, 83055854601

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Column 6 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +a(n-2) +8*a(n-3) -5*a(n-5) -17*a(n-6) -2*a(n-7) +6*a(n-8) +10*a(n-9) +a(n-10) -a(n-11) +a(n-12) -a(n-14) -a(n-15) for n>26

A302162 Number of nX7 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

21, 185, 56, 206, 603, 1247, 2853, 6870, 15489, 35924, 84962, 195967, 453837, 1061993, 2464882, 5719363, 13329296, 30988342, 71989905, 167525699, 389592291, 905597726, 2106327411, 4898465680, 11389209332, 26486000403, 61593726193

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Column 7 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +a(n-2) +11*a(n-3) -7*a(n-4) -7*a(n-5) -41*a(n-6) +26*a(n-7) +17*a(n-8) +74*a(n-9) -59*a(n-10) -19*a(n-11) -73*a(n-12) +82*a(n-13) +11*a(n-14) +44*a(n-15) -69*a(n-16) -5*a(n-17) -23*a(n-18) +34*a(n-19) +3*a(n-20) +14*a(n-21) -9*a(n-22) -a(n-23) -6*a(n-24) +a(n-25) +a(n-27) for n>39

A302165 Number of 3Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 6, 7, 12, 20, 34, 56, 94, 156, 262, 436, 730, 1216, 2034, 3392, 5670, 9460, 15806, 26380, 44066, 73560, 122858, 205112, 342542, 571916, 955062, 1594660, 2662890, 4446320, 7424674, 12397424, 20701558, 34566948, 57720430, 96380668, 160937266

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Row 3 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +2*a(n-4) for n>6

A302166 Number of 4Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 10, 17, 29, 51, 109, 206, 407, 791, 1584, 3104, 6165, 12131, 24059, 47443, 93958, 185498, 367087, 725156, 1434386, 2834565, 5605574, 11079494, 21907412, 43304842, 85620318, 169257166, 334632998, 661534245, 1307869617, 2585565413, 5111662053

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Row 4 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +a(n-2) +8*a(n-4) -4*a(n-5) -4*a(n-6) -a(n-7) -22*a(n-8) +a(n-9) +5*a(n-10) +2*a(n-11) +28*a(n-12) +6*a(n-13) -3*a(n-14) -3*a(n-15) -17*a(n-16) -4*a(n-17) +2*a(n-18) +2*a(n-19) +4*a(n-20) -a(n-22) for n>23

A302167 Number of 5Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 21, 31, 73, 140, 296, 603, 1288, 2584, 5456, 11189, 23561, 48423, 101409, 209594, 438175, 906900, 1891425, 3921725, 8172996, 16960434, 35311533, 73325262, 152605472, 317023164, 659531459, 1370465497, 2850564339, 5924450361

Offset: 1

R. H. Hardin, Apr 02 2018

nonn

Row 5 of A302163.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A302163.

Empirical: a(n) = a(n-1) +2*a(n-2) -a(n-3) +14*a(n-4) -10*a(n-5) -23*a(n-6) +5*a(n-7) -71*a(n-8) +44*a(n-9) +102*a(n-10) -14*a(n-11) +176*a(n-12) -115*a(n-13) -236*a(n-14) +43*a(n-15) -217*a(n-16) +199*a(n-17) +322*a(n-18) -95*a(n-19) +74*a(n-20) -223*a(n-21) -283*a(n-22) +111*a(n-23) +131*a(n-24) +140*a(n-25) +177*a(n-26) -75*a(n-27) -164*a(n-28) -39*a(n-29) -78*a(n-30) +40*a(n-31) +64*a(n-32) +6*a(n-33) +16*a(n-34) -12*a(n-35) -8*a(n-36) for n>40

cp's OEIS Frontend

A302164 Number of 2Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302157 Number of n X n 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302158 Number of nX3 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302159 Number of nX4 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302160 Number of nX5 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302161 Number of nX6 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302162 Number of nX7 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302165 Number of 3Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A302166 Number of 4Xn 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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