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 12 results. Next

A269283 Number of n X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

4, 216, 62748, 87559668, 598478857956, 20680187784811380, 3689070798270477232620, 3444847181845510308844394628, 16998439594375033474993893597991428
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Comments

Diagonal of A269289.

Examples

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

Links

Crossrefs

Cf. A269289.

A269284 Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

60, 2124, 62748, 1698732, 43674876, 1085203980, 26317946844, 626778812268, 14718495557052, 341767357185996, 7863372461151900, 179542238849355564, 4073026776304945788, 91888997272241919372, 2063133077083679521116
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Examples

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

Links

Crossrefs

Column 3 of A269289.

Formula

Empirical: a(n) = 42*a(n-1) - 441*a(n-2).
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: 12*x*(5 - 33*x) / (1 - 21*x)^2.
a(n) = 4 * 3^n * 7^(n-2) * (24*n+11).
(End)

A269285 Number of n X 4 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

216, 19188, 1363572, 87559668, 5306911092, 309846524148, 17623065834612, 983118947312628, 54032675767734132, 2934733632740325108, 157871441490222209652, 8425105813832255961588, 446611038737537558861172
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Examples

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

Links

Crossrefs

Column 4 of A269289.

Formula

Empirical: a(n) = 98*a(n-1) - 2401*a(n-2) for n>3.
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: 36*x*(1 - x)*(6 - 49*x) / (1 - 49*x)^2.
a(n) = 36 * (49^(n-2) * (240*n+53)) for n>1.
(End)

A269286 Number of n X 5 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

756, 164556, 27788292, 4204943820, 598478857956, 81907569617580, 10908770041709316, 1424067311317705740, 183070424003703987492, 23250470194285817181804, 2923940806264087088770116
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Examples

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

Links

Crossrefs

Column 5 of A269289.

Formula

Empirical: a(n) = 234*a(n-1) - 14277*a(n-2) + 68796*a(n-3) - 86436*a(n-4).
Empirical g.f.: 252*x*(3 - 49*x + 300*x^2 - 636*x^3) / (1 - 117*x + 294*x^2)^2. - Colin Barker, Jan 21 2019

A269287 Number of nX6 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

2592, 1363572, 544118148, 193446959076, 64538382287988, 20680187784811380, 6444304707617709156, 1967513283560471350788, 591384314583314302090068, 175574678705837994574453140, 51607712999525045688100012356
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Comments

Column 6 of A269289.

Examples

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

Links

Crossrefs

Cf. A269289.

Formula

Empirical: a(n) = 564*a(n-1) -87462*a(n-2) +2257724*a(n-3) -21169617*a(n-4) +76236552*a(n-5) -92236816*a(n-6) for n>7

A269288 Number of nX7 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

8748, 11026764, 10363900428, 8642330207532, 6751724437907820, 5062027330721456172, 3689070798270477232620, 2633315774277280991138604, 1850184391068250712299997676, 1283831257986363807652886516268
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Comments

Column 7 of A269289.

Examples

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

Links

Crossrefs

Cf. A269289.

Formula

Empirical: a(n) = 1384*a(n-1) -566002*a(n-2) +61993580*a(n-3) -3083170217*a(n-4) +82564587476*a(n-5) -1288497445564*a(n-6) +12048887832352*a(n-7) -66380108132464*a(n-8) +198314583195456*a(n-9) -247475435747904*a(n-10) for n>11

A269290 Number of 2 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

16, 216, 2124, 19188, 164556, 1363572, 11026764, 87559668, 685523916, 5306911092, 40706083404, 309846524148, 2343253251276, 17623065834612, 131903512372044, 983118947312628, 7300393156146636, 54032675767734132, 398738196097092684
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Examples

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

Links

Crossrefs

Row 2 of A269289.

Formula

Empirical: a(n) = 14*a(n-1) - 49*a(n-2) for n>4.
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: 4*x*(4 - 2*x - 29*x^2 + 9*x^3) / (1 - 7*x)^2.
a(n) = 36 * 7^(n-4) * (120*n+53) for n>2.
(End)

A269291 Number of 3 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

64, 2592, 62748, 1363572, 27788292, 544118148, 10363900428, 193439931300, 3554908340004, 64533455294868, 1159917367905324, 20677732339697748, 366084589527655236, 6443257191283855908, 112830460117748363340
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Examples

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

Links

Crossrefs

Row 3 of A269289.

Formula

Empirical: a(n) = 36*a(n-1) - 378*a(n-2) + 972*a(n-3) - 729*a(n-4) for n>7.
Empirical g.f.: 4*x*(16 + 72*x - 1593*x^2 + 5553*x^3 - 13581*x^4 + 17091*x^5 - 6804*x^6) / (1 - 18*x + 27*x^2)^2. - Colin Barker, Jan 21 2019

A269292 Number of 4Xn 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

256, 29160, 1698732, 87559668, 4204943820, 193446959076, 8642330207532, 377958654569412, 16263720330382476, 690974658284107428, 29056221832723692012, 1211537520551702429316, 50159175757694154381132
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Comments

Row 4 of A269289.

Examples

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

Links

Crossrefs

Cf. A269289.

Formula

Empirical: a(n) = 96*a(n-1) -3108*a(n-2) +40720*a(n-3) -265326*a(n-4) +931200*a(n-5) -1766452*a(n-6) +1678992*a(n-7) -622521*a(n-8) for n>12

A269293 Number of 5Xn 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

1024, 314928, 43674876, 5306911092, 598478857956, 64538382287988, 6751724437907820, 691013309706097812, 69557358002931376452, 6911040753656957427300, 679500524238978108503340
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2016

Keywords

Comments

Row 5 of A269289.

Examples

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

Links

Crossrefs

Cf. A269289.

Formula

Empirical: a(n) = 262*a(n-1) -25913*a(n-2) +1271424*a(n-3) -36373480*a(n-4) +662028380*a(n-5) -8018113210*a(n-6) +65608158980*a(n-7) -356568260410*a(n-8) +1185405035940*a(n-9) -1609856308508*a(n-10) -4162483461884*a(n-11) +23709461283851*a(n-12) -40474763971218*a(n-13) +272846513475*a(n-14) +106799477038956*a(n-15) -171480164894532*a(n-16) +115612142099328*a(n-17) -29562621871104*a(n-18) for n>23
Showing 1-10 of 12 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.