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 1-9 of 9 results.

A207736 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 16, 114, 1849, 86355, 9259849, 2215586241, 1207251562500, 1504250577851460, 4240840118917220289, 26956572348445823078057, 387211891430119861291459849, 12581321412478916326490284012715, 923581786817019708657060682986420624
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Diagonal of A207741

Examples

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

A207737 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

9, 81, 361, 1849, 10201, 58081, 335241, 1946025, 11323225, 65950641, 384277609, 2239466329, 13051920025, 76070604481, 443368207881, 2584130195529, 15061392571801, 87784176001041, 511643544572521, 2982076804476025
Offset: 1

Views

Author

R. H. Hardin, Feb 19 2012

Keywords

Comments

Column 4 of A207741.

Examples

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

Crossrefs

Cf. A207741.

Formula

Empirical: a(n) = 8*a(n-1) -11*a(n-2) -12*a(n-3) +13*a(n-4) +4*a(n-5) -a(n-6) for n>7.
Empirical g.f.: x*(9 + 9*x - 188*x^2 - 40*x^3 + 235*x^4 + 55*x^5 - 16*x^6) / ((1 - x)*(1 + x)*(1 - 6*x + x^2)*(1 - 2*x - x^2)). - Colin Barker, Jun 25 2018

A207738 Number of nX5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

15, 225, 1425, 10535, 86355, 733363, 6349893, 55343835, 484078805, 4239251331, 37149155225, 325617022405, 2854427890525, 25023592056775, 219376652808375, 1923245408892489, 16860907224450661, 147818180556775365
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Column 5 of A207741

Examples

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

Formula

Empirical: a(n) = 12*a(n-1) -2*a(n-2) -307*a(n-3) +431*a(n-4) +2588*a(n-5) -3497*a(n-6) -10961*a(n-7) +10555*a(n-8) +24977*a(n-9) -14239*a(n-10) -30241*a(n-11) +8813*a(n-12) +19175*a(n-13) -2139*a(n-14) -6107*a(n-15) +82*a(n-16) +903*a(n-17) +13*a(n-18) -56*a(n-19) +a(n-21) for n>22

A207739 Number of nX6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

25, 625, 5625, 60025, 731025, 9259849, 120275089, 1573946929, 20694836449, 272495484121, 3591309255625, 47344514140225, 624257470671025, 8231565447600625, 108546609662015625, 1431380241299659849
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Column 6 of A207741

Examples

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

Formula

Empirical: a(n) = 18*a(n-1) -15*a(n-2) -886*a(n-3) +2660*a(n-4) +11504*a(n-5) -45589*a(n-6) -59632*a(n-7) +324536*a(n-8) +106556*a(n-9) -1182417*a(n-10) +142992*a(n-11) +2369549*a(n-12) -855890*a(n-13) -2672392*a(n-14) +1338432*a(n-15) +1706837*a(n-16) -1018340*a(n-17) -603507*a(n-18) +418566*a(n-19) +106712*a(n-20) -93358*a(n-21) -5923*a(n-22) +10536*a(n-23) -500*a(n-24) -506*a(n-25) +51*a(n-26) +8*a(n-27) -a(n-28) for n>29

A207740 Number of nX7 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

40, 1600, 20550, 327075, 5959350, 113534330, 2215586241, 43590708750, 861389821740, 17048067532895, 337683209581900, 6690732833251660, 132588872475506025, 2627640756847273700, 52076089665529539750
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Column 7 of A207741

Examples

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

Formula

Empirical: a(n) = 32*a(n-1) -74*a(n-2) -5681*a(n-3) +36864*a(n-4) +379616*a(n-5) -3347394*a(n-6) -12764584*a(n-7) +148257198*a(n-8) +243956822*a(n-9) -3971669976*a(n-10) -2702550914*a(n-11) +71137025286*a(n-12) +14429838852*a(n-13) -901839561612*a(n-14) +34210546254*a(n-15) +8384954113963*a(n-16) -1284041429092*a(n-17) -58527272538120*a(n-18) +11728012112339*a(n-19) +311652839928564*a(n-20) -66235506274270*a(n-21) -1280749779000102*a(n-22) +267753041542212*a(n-23) +4098072327114980*a(n-24) -824906375480790*a(n-25) -10282688460625516*a(n-26) +2006945718348092*a(n-27) +20350191628061686*a(n-28) -3931453373643736*a(n-29) -31912328722759350*a(n-30) +6246115144236038*a(n-31) +39785076954556856*a(n-32) -8041469012168886*a(n-33) -39511371747893882*a(n-34) +8349334794212592*a(n-35) +31278208717969682*a(n-36) -6951475961437730*a(n-37) -19722109387644368*a(n-38) +4616459206223570*a(n-39) +9883326934842532*a(n-40) -2433800045758944*a(n-41) -3921613646635774*a(n-42) +1013855557594116*a(n-43) +1225356648569932*a(n-44) -331967762868842*a(n-45) -299264224053538*a(n-46) +84878286390780*a(n-47) +56566411518117*a(n-48) -16802393821234*a(n-49) -8169166554058*a(n-50) +2546494699357*a(n-51) +886299569042*a(n-52) -291138166440*a(n-53) -70640787008*a(n-54) +24626038986*a(n-55) +4013666266*a(n-56) -1501723992*a(n-57) -156022566*a(n-58) +63735634*a(n-59) +3920928*a(n-60) -1790714*a(n-61) -59044*a(n-62) +30840*a(n-63) +489*a(n-64) -284*a(n-65) -2*a(n-66) +a(n-67) for n>68

A207742 Number of 4Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

9, 81, 387, 1849, 10535, 60025, 327075, 1782225, 9840285, 54331641, 298827711, 1643572681, 9050656627, 49839223009, 274344889595, 1510158343225, 8313840821405, 45770001214609, 251966391900979, 1387088943911449
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 4 of A207741

Examples

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

Formula

Empirical: a(n) = 4*a(n-1) +32*a(n-3) +132*a(n-4) -238*a(n-5) -136*a(n-6) -1068*a(n-7) -3958*a(n-8) +5414*a(n-9) +7248*a(n-10) +3912*a(n-11) +23868*a(n-12) -23346*a(n-13) -29268*a(n-14) -4140*a(n-15) -61497*a(n-16) +37350*a(n-17) +24948*a(n-18) -5400*a(n-19) +52920*a(n-20) -33264*a(n-21) -2592*a(n-22) -11664*a(n-24) +7776*a(n-25)

A207743 Number of 5Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

14, 196, 1414, 10201, 86355, 731025, 5959350, 48580900, 400851670, 3307515121, 27172739769, 223236405441, 1837212857466, 15120074510116, 124343788256622, 1022572849602249, 8412135030604107, 69201930992634801, 569203250129458902
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 5 of A207741

Examples

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

A207744 Number of 6Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

22, 484, 5302, 58081, 733363, 9259849, 113534330, 1392036100, 17213677390, 212861354161, 2624875417711, 32368350683761, 399547127975296, 4931913554477056, 60855630257333632, 750906862642685329
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 6 of A207741

Examples

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

A207745 Number of 7Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

35, 1225, 20265, 335241, 6349893, 120275089, 2215586241, 40813292529, 758253127923, 14087268396601, 260910039667519, 4832310060602761, 89611728280729061, 1661785304492145361, 30800180353416930867
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 7 of A207741

Examples

			Some solutions for n=4
..1..1..1..1....1..1..1..0....1..1..0..0....1..0..1..1....0..1..1..0
..1..1..1..1....0..1..1..1....1..1..0..0....1..1..0..1....1..1..1..0
..1..1..1..0....1..0..0..1....1..1..0..0....1..1..1..1....0..1..1..0
..1..0..1..1....0..1..1..1....1..1..0..0....0..1..1..0....1..1..1..0
..1..1..0..1....1..0..0..1....1..1..0..0....1..0..1..1....1..1..0..0
..0..1..1..1....0..1..1..0....1..1..0..0....0..1..1..0....0..1..1..0
..1..0..0..1....1..1..1..1....1..1..0..0....1..0..1..1....1..1..0..0
		
Showing 1-9 of 9 results.