A278208 -id:A278208 - cp's OEIS frontend

A278203 Number of n X 3 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

0, 15, 97, 666, 4827, 34869, 251260, 1811189, 13056663, 94122538, 678506791, 4891196693, 35259493158, 254177432493, 1832305613593, 13208662283862, 95218154664535, 686405389318065, 4948135785116200, 35669952667919773

Offset: 1

R. H. Hardin, Nov 15 2016

nonn

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

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

Column 3 of A278208.

Empirical: a(n) = 6*a(n-1) + 7*a(n-2) + 11*a(n-3) + 11*a(n-4) - 9*a(n-5) + 3*a(n-7) - 2*a(n-8) for n>9.

Empirical g.f.: x^2*(15 + 7*x - 21*x^2 - 13*x^3 + 13*x^4 - x^5 - 4*x^6 + 2*x^7) / (1 - 6*x - 7*x^2 - 11*x^3 - 11*x^4 + 9*x^5 - 3*x^7 + 2*x^8). - Colin Barker, Feb 09 2019

A278204 Number of nX4 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

Original entry on oeis.org

0, 46, 666, 8242, 117088, 1674402, 23732454, 336380248, 4770344900, 67648850802, 959306211222, 13603641359640, 192909619956550, 2735599405114814, 38792794983910750, 550110139019848618, 7800963216380203384

Offset: 1

R. H. Hardin, Nov 15 2016

nonn

Column 4 of A278208.

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

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

Cf. A278208.

Empirical: a(n) = 10*a(n-1) +46*a(n-2) +157*a(n-3) +471*a(n-4) -202*a(n-5) -2198*a(n-6) -1400*a(n-7) -941*a(n-8) -1959*a(n-9) +2763*a(n-10) +374*a(n-11) -387*a(n-12) +3427*a(n-13) -1743*a(n-14) -335*a(n-15) +862*a(n-16) -1124*a(n-17) +584*a(n-18) -96*a(n-19)

A278205 Number of nX5 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

Original entry on oeis.org

0, 161, 4827, 117088, 3295771, 93838003, 2644587148, 74502577363, 2100207846025, 59204820850114, 1668914682945041, 47044781998461473, 1326141579240041036, 37382494487271576091, 1053771855874680878859, 29704682675479642221344

Offset: 1

R. H. Hardin, Nov 15 2016

nonn

Column 5 of A278208.

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

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

Cf. A278208.

Empirical: a(n) = 19*a(n-1) +189*a(n-2) +1584*a(n-3) +10608*a(n-4) +14412*a(n-5) -85090*a(n-6) -391138*a(n-7) -1606034*a(n-8) -2817596*a(n-9) +5687406*a(n-10) +8027881*a(n-11) +19438705*a(n-12) +68401755*a(n-13) -31364868*a(n-14) -61559855*a(n-15) -91683401*a(n-16) -479455372*a(n-17) +12586341*a(n-18) -58748050*a(n-19) -86449447*a(n-20) +1397633647*a(n-21) -203563888*a(n-22) +375197049*a(n-23) +833933492*a(n-24) -1926809978*a(n-25) +421547099*a(n-26) -230101783*a(n-27) -639000471*a(n-28) +809196262*a(n-29) +51478617*a(n-30) -9474388*a(n-31) -240861719*a(n-32) +36942959*a(n-33) +34157730*a(n-34) -3062038*a(n-35) +203994920*a(n-36) -123672724*a(n-37) -22260448*a(n-38) +9217234*a(n-39) -17678304*a(n-40) +15339168*a(n-41) +1345364*a(n-42) -884528*a(n-43) -95208*a(n-44) -422416*a(n-45) +21888*a(n-46) +7488*a(n-47) +17280*a(n-48) for n>49

A278206 Number of nX6 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

Original entry on oeis.org

0, 601, 34869, 1674402, 93838003, 5306819216, 297169006604, 16636687338399, 931945034345185, 52205261260655693, 2924300169544392520, 163806092390120341088, 9175698877050626080778, 513982345733812946152984

Offset: 1

R. H. Hardin, Nov 15 2016

nonn

Column 6 of A278208.

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

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

Cf. A278208.

A278207 Number of nX7 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

Original entry on oeis.org

0, 2208, 251260, 23732454, 2644587148, 297169006604, 33056811286568, 3676498268449668, 409137247202506544, 45530553691308851854, 5066646847508250491070, 563817868393293695820130

Offset: 1

R. H. Hardin, Nov 15 2016

nonn

Column 7 of A278208.

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

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

Cf. A278208.

A278202 Number of n X n 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1), (-1,0), (-1,1), (0,-1), (0,1), (1,-1), (1,0) or (1,1), with upper left element zero.

Original entry on oeis.org

0, 3, 97, 8242, 3295771, 5306819216, 33056811286568, 812312404546266967, 78877646007318566942149, 30229204386668969418436705255, 45720403850059908972915757270717926

Offset: 1

R. H. Hardin, Nov 15 2016

nonn

Diagonal of A278208.

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

Cf. A278208.

cp's OEIS Frontend

A278203 Number of n X 3 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

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A278204 Number of nX4 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

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A278205 Number of nX5 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

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A278206 Number of nX6 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

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A278207 Number of nX7 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

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A278202 Number of n X n 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1), (-1,0), (-1,1), (0,-1), (0,1), (1,-1), (1,0) or (1,1), with upper left element zero.

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