A280961 -id:A280961 - cp's OEIS frontend

A280955 Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

2, 9, 42, 205, 997, 4850, 23593, 114769, 558298, 2715861, 13211405, 64267362, 312630929, 1520804569, 7398009354, 35987886621, 175064388469, 851607109714, 4142673879353, 20152188344737, 98031056006074, 476875651282597

Offset: 1

R. H. Hardin, Jan 11 2017

nonn

			Some solutions for n=4:
..0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..0. .0..0. .0..1. .0..1
..0..2. .2..0. .1..2. .2..1. .2..2. .2..2. .1..1. .1..2. .2..2. .2..0
..1..0. .1..2. .0..2. .0..2. .1..0. .1..0. .2..2. .2..0. .1..0. .0..1
..0..1. .0..0. .1..1. .1..0. .1..0. .2..2. .0..1. .1..1. .0..2. .2..1

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

Column 2 of A280961.

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

Empirical g.f.: x*(1 - x)*(1 + x)*(2 + x) / (1 - 4*x - 4*x^2 - x^3). - Colin Barker, Feb 15 2019

A280956 Number of nX3 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

4, 42, 241, 1554, 9899, 63085, 402077, 2562733, 16334111, 104108376, 663554669, 4229292041, 26956196587, 171810442122, 1095066516245, 6979614612419, 44485900541127, 283539343806484, 1807191908208865, 11518481171610485

Offset: 1

R. H. Hardin, Jan 11 2017

nonn

Column 3 of A280961.

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

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

Cf. A280961.

Empirical: a(n) = 5*a(n-1) +8*a(n-2) +5*a(n-3) +4*a(n-4) -35*a(n-5) +2*a(n-6) +71*a(n-7) -11*a(n-8) -38*a(n-9) +6*a(n-10) -8*a(n-11) -8*a(n-12) for n>16

A280957 Number of nX4 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

11, 205, 1554, 14106, 126267, 1121528, 9986376, 88940022, 791997382, 7052519878, 62801413162, 559236961207, 4979918315253, 44345374930680, 394888443546716, 3516418473800700, 31313145020210260, 278838553941378885

Offset: 1

R. H. Hardin, Jan 11 2017

nonn

Column 4 of A280961.

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

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

Cf. A280961.

Empirical: a(n) = 11*a(n-1) -25*a(n-2) +62*a(n-3) +6*a(n-4) -470*a(n-5) -199*a(n-6) -97*a(n-7) +1761*a(n-8) +1271*a(n-9) -4651*a(n-10) +16916*a(n-11) +28022*a(n-12) -48991*a(n-13) -17485*a(n-14) +9764*a(n-15) -403040*a(n-16) -181089*a(n-17) +1006721*a(n-18) +635719*a(n-19) -545439*a(n-20) +450907*a(n-21) +419840*a(n-22) -1904900*a(n-23) -1409770*a(n-24) +462471*a(n-25) -68469*a(n-26) -393605*a(n-27) +577614*a(n-28) +1161352*a(n-29) +807943*a(n-30) +65475*a(n-31) -70526*a(n-32) -17768*a(n-33) -450612*a(n-34) -560853*a(n-35) -288048*a(n-36) +109569*a(n-37) +243445*a(n-38) +191920*a(n-39) +25889*a(n-40) -30729*a(n-41) -31913*a(n-42) -14398*a(n-43) -9025*a(n-44) +830*a(n-45) +2189*a(n-46) +2423*a(n-47) +167*a(n-48) -140*a(n-49) -187*a(n-50) +2*a(n-51) +10*a(n-52) +4*a(n-53) -a(n-54) for n>57

A280958 Number of n X 5 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

30, 997, 9899, 126267, 1599234, 20029500, 251270618, 3152475854, 39530438497, 495721552160, 6216700479112, 77962372076794, 977711970478121, 12261314459515967, 153766955348557489, 1928363669762835672

Offset: 1

R. H. Hardin, Jan 11 2017

nonn

Column 5 of A280961.

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

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

Cf. A280961.

A280959 Number of nX6 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

82, 4850, 63085, 1121528, 20029500, 346289502, 6052621154, 105777297118, 1846875100200, 32253949107668, 563278827019060, 9836989060923111, 171791531487108414, 3000138481060751984, 52393917402743354484

Offset: 1

R. H. Hardin, Jan 11 2017

nonn

Column 6 of A280961.

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

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

Cf. A280961.

A280960 Number of nX7 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

224, 23593, 402077, 9986376, 251270618, 6052621154, 148137367471, 3624578433814, 88500510514256, 2162800206884214, 52848406746190667, 1291317121466531838, 31553229218022226192, 770996700142671487457

Offset: 1

R. H. Hardin, Jan 11 2017

nonn

Column 7 of A280961.

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

R. H. Hardin, Table of n, a(n) for n = 1..62

Cf. A280961.

cp's OEIS Frontend

A280955 Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280956 Number of nX3 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280957 Number of nX4 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280958 Number of n X 5 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280959 Number of nX6 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280960 Number of nX7 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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Keywords

Comments

Examples

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