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.

A203979 Number of (n+1)X4 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

96, 864, 7776, 69984, 629856, 5668704, 51018336, 459165024, 4132485216, 37192366944, 334731302496, 3012581722464, 27113235502176, 244019119519584, 2196172075676256, 19765548681086304, 177889938129776736
Offset: 1

Views

Author

R. H. Hardin Jan 09 2012

Keywords

Comments

Column 3 of A203984

Examples

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

Formula

Empirical: a(n) = 96*9^(n-1)

A203980 Number of (n+1) X 5 0..2 arrays with no 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

384, 5184, 69984, 956448, 13071456, 178855776, 2447270496, 33489653472, 458288894304, 6271519652064, 85823503984224, 1174465206026208, 16072153386090336, 219941927082883296, 3009830115907061856
Offset: 1

Views

Author

R. H. Hardin, Jan 09 2012

Keywords

Comments

Column 4 of A203984.

Examples

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

Crossrefs

Cf. A203984.

Formula

Empirical: a(n) = 15*a(n-1) - 270*a(n-3) + 324*a(n-4).
Empirical g.f.: 96*x*(4 - 6*x - 81*x^2 + 108*x^3) / ((1 - 15*x + 18*x^2)*(1 - 18*x^2)). - Colin Barker, Jun 06 2018

A203981 Number of (n+1) X 6 0..2 arrays with no 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

1536, 31104, 629856, 13071456, 271918944, 5671161216, 118333620576, 2469841766784, 51553851826176, 1076137623724896, 22463572543638624, 468912308350736736, 9788249148960940416, 204323642334833818464
Offset: 1

Views

Author

R. H. Hardin, Jan 09 2012

Keywords

Comments

Column 5 of A203984.

Examples

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

Crossrefs

Cf. A203984.

Formula

Empirical: a(n) = 25*a(n-1) - 45*a(n-2) - 963*a(n-3) + 2025*a(n-4) + 3645*a(n-5) - 6561*a(n-6).
Empirical g.f.: 96*x*(16 - 76*x - 819*x^2 + 2124*x^3 + 3321*x^4 - 6561*x^5) / ((1 - 25*x + 90*x^2 - 81*x^3)*(1 - 45*x^2 - 81*x^3)). - Colin Barker, Jun 06 2018

A203982 Number of (n+1)X7 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

6144, 186624, 5668704, 178855776, 5671161216, 180709558848, 5764846339584, 184042295652096, 5876808948959616, 187680079115373888, 5993929440264576384, 191431738781962474176, 6113912564634046252416, 195265725121889159876928
Offset: 1

Views

Author

R. H. Hardin Jan 09 2012

Keywords

Comments

Column 6 of A203984

Examples

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

Formula

Empirical: a(n) = 39*a(n-1) +117*a(n-2) -13419*a(n-3) +42120*a(n-4) +1465776*a(n-5) -7558272*a(n-6) -59591376*a(n-7) +389959596*a(n-8) +776691180*a(n-9) -7353962460*a(n-10) -230291100*a(n-11) +53356676400*a(n-12) -41452398000*a(n-13) -124357194000*a(n-14) +143489070000*a(n-15)

A203983 Number of (n+1)X8 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

24576, 1119744, 51018336, 2447270496, 118333620576, 5764846339584, 281455764775776, 13760034485954400, 673045752535673184, 32929530583286102400, 1611290252343314405376, 78847099619621520230496
Offset: 1

Views

Author

R. H. Hardin Jan 09 2012

Keywords

Comments

Column 7 of A203984

Examples

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

Formula

Empirical: a(n) = 81*a(n-1) -990*a(n-2) -55557*a(n-3) +1308051*a(n-4) +9877815*a(n-5) -472364460*a(n-6) +943100415*a(n-7) +77404069476*a(n-8) -518255160660*a(n-9) -6362605755783*a(n-10) +72333960423075*a(n-11) +223601505317082*a(n-12) -5264665776830025*a(n-13) +3575284914586527*a(n-14) +225704467607414148*a(n-15) -691301950951353183*a(n-16) -5753524457427090471*a(n-17) +31302036027799741413*a(n-18) +76304508958149193188*a(n-19) -780598320639827527251*a(n-20) -32107509630606372660*a(n-21) +11916298097181567343665*a(n-22) -16999232257151001851004*a(n-23) -110708791324500349192293*a(n-24) +303730479433392729885693*a(n-25) +555754575465898156952694*a(n-26) -2737618881639491778320259*a(n-27) -584755510344811831795446*a(n-28) +14407869192888759424255026*a(n-29) -9579065689150601713125282*a(n-30) -44620541811711898638722874*a(n-31) +59888834204786049381681870*a(n-32) +75210686676036004338582552*a(n-33) -168955611080998044775817142*a(n-34) -43167918621829199898820959*a(n-35) +262083277346193044061068880*a(n-36) -64367087618676610768687146*a(n-37) -218976915013228373921343981*a(n-38) +130739067080067867741115677*a(n-39) +78915491598396738245792607*a(n-40) -84109173336513103888007001*a(n-41) +3118769447215496774534127*a(n-42) +17814505620501527202817290*a(n-43) -6540848332303545808795602*a(n-44) +717897987691852588770249*a(n-45)

A203978 Number of (n+1)X(n+1) 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

6, 144, 7776, 956448, 271918944, 180709558848, 281455764775776, 1031010515432951328, 8894627860916158754400, 180980943906416856129607680
Offset: 1

Views

Author

R. H. Hardin Jan 09 2012

Keywords

Comments

Diagonal of A203984

Examples

			Some solutions for n=4
..0..1..0..2..1....0..1..1..1..1....0..0..0..1..1....0..0..0..0..1
..2..1..0..2..0....2..2..2..2..0....2..2..2..2..2....1..1..1..2..1
..0..1..0..2..0....1..0..1..1..0....0..0..0..0..1....0..0..0..0..0
..2..1..0..1..1....1..0..2..2..2....1..1..1..2..1....1..2..1..1..1
..2..1..0..2..2....1..0..1..0..1....0..2..0..2..0....1..2..0..2..2
		
Showing 1-6 of 6 results.