A239819 -id:A239819 - cp's OEIS frontend

A239812 Number of n X 1 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

2, 5, 11, 25, 57, 129, 293, 665, 1509, 3425, 7773, 17641, 40037, 90865, 206221, 468025, 1062197, 2410689, 5471133, 12416905, 28180549, 63956625, 145151533, 329425881, 747642197, 1696797025, 3850933181, 8739811625, 19835272037, 45016761649

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Column 1 of A239819.

			Some solutions for n=5:
..2....2....2....2....3....2....2....3....2....3....2....2....3....3....2....3
..1....1....2....2....1....1....1....3....2....1....1....1....2....3....2....2
..3....2....3....2....2....3....2....2....2....3....2....3....1....1....2....3
..1....1....2....1....1....1....3....3....1....3....1....1....1....3....2....2
..1....2....1....2....1....3....3....3....3....1....1....2....2....1....3....2

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

Cf. A239819.

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

Empirical g.f.: x*(2 + 3*x + 2*x^2) / (1 - x - 2*x^2 - 2*x^3). - Colin Barker, Feb 21 2018

A239813 Number of nX2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

Original entry on oeis.org

4, 23, 113, 582, 2981, 15266, 78188, 400542, 2051667, 10509067, 53831920, 275740995, 1412438656, 7234951864, 37059718148, 189831642853, 972377820507, 4980827553280, 25513377870835, 130687610786192, 669423377137934

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Column 2 of A239819

			Some solutions for n=5
..2..0....2..0....2..0....3..2....3..2....3..0....3..0....3..2....2..3....2..0
..1..3....2..3....2..3....3..2....3..2....1..2....2..0....1..0....2..3....1..0
..3..2....3..1....3..1....2..3....1..0....2..0....1..3....3..2....2..0....3..0
..1..3....1..0....3..2....3..2....1..2....1..2....1..2....3..2....1..2....1..3
..2..3....3..0....1..2....1..3....2..0....1..0....1..3....2..1....2..0....1..3

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

Empirical: a(n) = a(n-1) +16*a(n-2) +31*a(n-3) -8*a(n-4) -78*a(n-5) -45*a(n-6) +56*a(n-7) -32*a(n-8) +32*a(n-9) +16*a(n-10)

A239814 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

Original entry on oeis.org

10, 132, 1480, 17552, 204779, 2405330, 28156167, 330152684, 3868656623, 45340827197, 531385036815, 6227630455564, 72986367133614, 855377894814551, 10024792297748632, 117487669001323549, 1376922218413007325

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Column 3 of A239819

			Some solutions for n=4
..3..2..0....3..2..2....3..2..3....3..0..0....3..2..2....3..0..0....2..0..3
..1..2..0....1..0..2....1..2..2....2..3..0....1..0..2....2..0..0....1..3..2
..3..0..2....3..0..2....3..2..0....3..1..3....3..2..3....1..0..2....3..1..3
..3..0..0....2..0..0....1..2..0....2..3..3....1..3..2....2..0..0....2..0..0

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

Empirical: a(n) = 2*a(n-1) +103*a(n-2) +305*a(n-3) -1576*a(n-4) -7517*a(n-5) +13822*a(n-6) +84263*a(n-7) -193487*a(n-8) -386588*a(n-9) +2125542*a(n-10) -2240531*a(n-11) -6903934*a(n-12) +24598571*a(n-13) -24037070*a(n-14) -20933507*a(n-15) +84761410*a(n-16) -76409880*a(n-17) -58972949*a(n-18) +191904430*a(n-19) -103074732*a(n-20) -119505780*a(n-21) +301528072*a(n-22) -71474328*a(n-23) -220257104*a(n-24) +158665984*a(n-25) -141276800*a(n-26) -317537024*a(n-27) -19131392*a(n-28) -71272448*a(n-29) -128999424*a(n-30) -20832256*a(n-31) -5177344*a(n-32) -4849664*a(n-33) +1048576*a(n-34) +524288*a(n-35)

A239815 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

Original entry on oeis.org

24, 729, 18728, 510748, 13597573, 366379173, 9807771898, 263419973152, 7064275271994, 189566431524540, 5085635223031781, 136450277248685119, 3660861731265982119, 98220442090411319757, 2635213560025173917109

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Column 4 of A239819

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

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

A239816 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

Original entry on oeis.org

56, 3951, 232272, 14544801, 884977259, 54668820459, 3347474694032, 205970817822022, 12641836066488239, 776862587801118702, 47711236158517841564, 2931070666588302434209, 180038209753070897538954

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Column 5 of A239819

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

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

A239817 Number of n X 6 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

Original entry on oeis.org

132, 21602, 2912793, 418324402, 58232200212, 8243207656791, 1154988223050638, 162794110794893005, 22871029907841066549, 3218700464551459701771, 452563580936326395762181, 63663914001474387730433692

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Column 6 of A239819.

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

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

Cf. A239819.

A239818 Number of nX7 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

Original entry on oeis.org

312, 118253, 36627126, 12059066460, 3842974545029, 1246285848518417, 399696014140196630, 129035213192353255123, 41500218830682985410810, 13375093569069190733883673, 4305661324527210642658505946

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Column 7 of A239819

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

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

A239820 Number of 2Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

5, 23, 132, 729, 3951, 21602, 118253, 646306, 3532732, 19315270, 105601487, 577330665, 3156353205, 17256335056, 94343160597, 515789128277, 2819903064231, 15416868881838, 84286524854294, 460808121256380, 2519312876415017

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Row 2 of A239819

			Some solutions for n=5
..3..0..0..0..0....3..2..3..2..3....3..0..0..2..3....3..0..2..0..2
..2..0..3..0..3....2..0..1..2..2....2..3..2..0..1....1..0..2..0..1

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

Empirical: a(n) = 9*a(n-1) -28*a(n-2) +74*a(n-3) -181*a(n-4) +236*a(n-5) -261*a(n-6) +234*a(n-7) +200*a(n-8) -279*a(n-9) +104*a(n-10) -268*a(n-11) -36*a(n-12) +156*a(n-13) +104*a(n-14) -32*a(n-15) -16*a(n-16)

A239821 Number of 3Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

11, 113, 1480, 18728, 232272, 2912793, 36627126, 459870638, 5774508494, 72538478424, 911227478673, 11446501405086, 143789611879946, 1806288798172920, 22690641341877163, 285040443527806965

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Row 3 of A239819

			Some solutions for n=4
..2..0..0..3....3..2..2..0....2..0..0..0....3..2..0..0....3..2..3..2
..1..2..0..1....2..0..0..0....1..3..2..0....1..0..0..0....3..2..2..0
..3..1..3..0....3..1..1..2....2..3..2..2....3..2..3..2....1..3..3..1

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 64

Empirical recurrence of order 64 (see link above)

A239822 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

25, 582, 17552, 510748, 14544801, 418324402, 12059066460, 347095468871, 9991360194005, 287711413471266, 8284928413145004, 238566125657445992, 6869701227384114007, 197820645386511819554, 5696463550662058123697

Offset: 1

R. H. Hardin, Mar 27 2014

nonn

Row 4 of A239819

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

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

cp's OEIS Frontend

A239812 Number of n X 1 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

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A239813 Number of nX2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

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A239814 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

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A239815 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

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A239816 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

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A239817 Number of n X 6 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

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A239818 Number of nX7 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.

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A239820 Number of 2Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.

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A239821 Number of 3Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.

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A239822 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.

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