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 1-6 of 6 results.

A207414 Number of nX3 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

6, 36, 92, 241, 720, 1889, 4719, 12102, 30414, 74588, 182737, 445468, 1075185, 2583413, 6187826, 14753420, 35052328, 83069841, 196345572, 462972905, 1089545883, 2559508250, 6002666694, 14057272936, 32876868289, 76799290072
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Column 3 of A207419

Examples

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

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +7*a(n-3) -21*a(n-4) +7*a(n-5) -a(n-6) +33*a(n-7) +7*a(n-8) -13*a(n-9) -35*a(n-10) -7*a(n-11) +9*a(n-12) +17*a(n-13) +4*a(n-14) -3*a(n-15) -3*a(n-16)

A207413 Number of n X n 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 16, 92, 742, 13260, 220882, 4094666, 129528304, 4643477356, 183171965504, 10948746139548, 797831881523648, 65446536338563458, 7746605907720894574, 1149785247198798823392, 195841032765969991278104
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Diagonal of A207419

Examples

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

A207415 Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

9, 81, 241, 742, 2760, 8465, 24317, 73405, 214117, 601411, 1698702, 4766632, 13156641, 36175599, 99198867, 270109351, 732494449, 1982055330, 5345239912, 14374634237, 38587852393, 103391960861, 276535572481, 738655032563
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Column 4 of A207419.

Examples

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

Crossrefs

Cf. A207419.

Formula

Empirical: a(n) = 5*a(n-1) -8*a(n-2) +23*a(n-3) -74*a(n-4) +70*a(n-5) -116*a(n-6) +362*a(n-7) -122*a(n-8) +152*a(n-9) -916*a(n-10) -166*a(n-11) +26*a(n-12) +1638*a(n-13) +657*a(n-14) -225*a(n-15) -1890*a(n-16) -895*a(n-17) +372*a(n-18) +1268*a(n-19) +486*a(n-20) -190*a(n-21) -454*a(n-22) -122*a(n-23) +60*a(n-24) +60*a(n-25).

A207416 Number of nX5 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

14, 196, 720, 2760, 13260, 50139, 175903, 656508, 2338562, 7964440, 27387966, 93272992, 311246157, 1035796645, 3435764764, 11296068814, 36992161254, 120875903016, 393346541394, 1276189913811, 4133174774211, 13356263152094
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Column 5 of A207419

Examples

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

Formula

Empirical: a(n) = 7*a(n-1) -18*a(n-2) +72*a(n-3) -303*a(n-4) +553*a(n-5) -1440*a(n-6) +4899*a(n-7) -5932*a(n-8) +12977*a(n-9) -41708*a(n-10) +25293*a(n-11) -68030*a(n-12) +222709*a(n-13) +1292*a(n-14) +276787*a(n-15) -815366*a(n-16) -465935*a(n-17) -1032664*a(n-18) +2055611*a(n-19) +2236058*a(n-20) +3161899*a(n-21) -3425378*a(n-22) -5665821*a(n-23) -6993506*a(n-24) +3611199*a(n-25) +8921806*a(n-26) +10534143*a(n-27) -2236191*a(n-28) -9255318*a(n-29) -10408700*a(n-30) +805371*a(n-31) +6396787*a(n-32) +6551264*a(n-33) -463326*a(n-34) -2910858*a(n-35) -2406262*a(n-36) +433824*a(n-37) +836762*a(n-38) +458312*a(n-39) -259060*a(n-40) -136464*a(n-41) -21136*a(n-42) +62656*a(n-43) +10816*a(n-44) -7680*a(n-46)

A207417 Number of nX6 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

21, 441, 1889, 8465, 50139, 220882, 891720, 3919354, 16153614, 62844340, 248939744, 971561382, 3682206767, 13939172767, 52509796817, 195002378289, 720554922955, 2654209247431, 9705662821905, 35326530765908, 128233462946586
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Column 6 of A207419

Examples

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

Formula

Empirical: a(n) = 7*a(n-1) -18*a(n-2) +133*a(n-3) -651*a(n-4) +1197*a(n-5) -6333*a(n-6) +25033*a(n-7) -28961*a(n-8) +163943*a(n-9) -540803*a(n-10) +237661*a(n-11) -2878759*a(n-12) +7368443*a(n-13) +2759841*a(n-14) +40040383*a(n-15) -63788653*a(n-16) -91689483*a(n-17) -468035403*a(n-18) +278011313*a(n-19) +1100089375*a(n-20) +4448328425*a(n-21) +890079235*a(n-22) -7473780937*a(n-23) -32664895543*a(n-24) -25093841639*a(n-25) +27574919869*a(n-26) +179897474619*a(n-27) +216007871867*a(n-28) -9756360635*a(n-29) -731446118553*a(n-30) -1168944414481*a(n-31) -509277673393*a(n-32) +2152826290459*a(n-33) +4473263365821*a(n-34) +3291115591779*a(n-35) -4365927221311*a(n-36) -12617420740547*a(n-37) -12111562452533*a(n-38) +5122275137275*a(n-39) +26678065154599*a(n-40) +30782154493137*a(n-41) +331721793983*a(n-42) -42473769486659*a(n-43) -57185244173887*a(n-44) -14818593702641*a(n-45) +50726821023071*a(n-46) +79319623488451*a(n-47) +32697961096541*a(n-48) -45037125484709*a(n-49) -82701165846535*a(n-50) -41748724592059*a(n-51) +29522057915419*a(n-52) +64840591966667*a(n-53) +35591391891735*a(n-54) -14632491527295*a(n-55) -38278407480750*a(n-56) -20781217384488*a(n-57) +6225156196823*a(n-58) +17254112391656*a(n-59) +8222659116728*a(n-60) -2816556374268*a(n-61) -6172556854972*a(n-62) -2148893110640*a(n-63) +1280732581092*a(n-64) +1832892162528*a(n-65) +363771285460*a(n-66) -440972445372*a(n-67) -439479423060*a(n-68) -33695710728*a(n-69) +97956064212*a(n-70) +74897224416*a(n-71) -4908530304*a(n-72) -15199461216*a(n-73) -8390305296*a(n-74) +2918078784*a(n-75) +2129706432*a(n-76) +925717248*a(n-77) -389608704*a(n-78) -194088960*a(n-79) -97044480*a(n-80)

A207418 Number of nX7 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

31, 961, 4719, 24317, 175903, 891720, 4094666, 21072638, 99746042, 440141222, 2003254604, 8937597494, 38381074339, 165425593855, 709144263593, 2981321572403, 12486729646315, 52162085656079, 215733902493821
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Column 7 of A207419

Examples

			Some solutions for n=4
..1..1..1..0..0..0..0....1..1..1..1..1..0..0....0..1..1..1..0..0..0
..0..1..1..1..0..0..0....1..1..1..0..0..0..0....1..1..1..0..1..1..0
..0..0..0..0..0..0..0....0..1..1..0..0..0..0....0..0..0..0..0..0..0
..1..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
		
Showing 1-6 of 6 results.