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 1-7 of 7 results.

A203974 Number of nX7 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

Original entry on oeis.org

44, 5569, 1107082, 180623180, 30104480870, 5061444598545, 847220834970347, 141937054743243405, 23779975312437117115, 3983658769957290205062, 667379066179974381638813, 111804522576410924713391638
Offset: 1

Views

Author

R. H. Hardin Jan 08 2012

Keywords

Comments

Column 7 of A203975

Examples

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

A203969 Number of n X 2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

Original entry on oeis.org

2, 7, 29, 106, 396, 1488, 5569, 20859, 78133, 292644, 1096125, 4105590, 15377699, 57598086, 215736791, 808054127, 3026612006, 11336343903, 42460908170, 159039700345, 595692067467, 2231197862121, 8357076036219, 31301894398172
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2012

Keywords

Comments

Column 2 of A203975.

Examples

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

Crossrefs

Cf. A203975.

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) +12*a(n-3) +4*a(n-4) +5*a(n-5) -9*a(n-6) -a(n-8) +a(n-9).
Empirical g.f.: x*(2 + 3*x + 9*x^2 + 3*x^3 + 5*x^4 - 8*x^5 - x^7 + x^8) / ((1 + x + x^2 - x^3)*(1 - 3*x - x^2 - 7*x^3 + x^4 + x^6)). - Colin Barker, Jun 06 2018

A203970 Number of nX3 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

Original entry on oeis.org

4, 29, 258, 2061, 16723, 136243, 1107082, 9001543, 73188575, 595039791, 4837958263, 39334611930, 319806460796, 2600161056897, 21140392838611, 171880201142842, 1397457732946504, 11361914049797193, 92377098701406680
Offset: 1

Views

Author

R. H. Hardin Jan 08 2012

Keywords

Comments

Column 3 of A203975

Examples

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

Formula

Empirical: a(n) = 4*a(n-1) +14*a(n-2) +134*a(n-3) +164*a(n-4) +465*a(n-5) -951*a(n-6) -633*a(n-7) -3451*a(n-8) +4286*a(n-9) +1728*a(n-10) +5640*a(n-11) -7916*a(n-12) -1912*a(n-13) -2947*a(n-14) +6073*a(n-15) +752*a(n-16) +143*a(n-17) -1899*a(n-18) +55*a(n-19) +89*a(n-20) +178*a(n-21) -5*a(n-22) -5*a(n-23) -5*a(n-24)

A203971 Number of nX4 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

Original entry on oeis.org

7, 106, 2061, 34799, 601521, 10443081, 180623180, 3127443494, 54147787428, 937401735877, 16229119258691, 280969835877155, 4864330622552017, 84214645085725068, 1457981042829787092, 25241554445266482645
Offset: 1

Views

Author

R. H. Hardin Jan 08 2012

Keywords

Comments

Column 4 of A203975

Examples

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

Formula

Empirical: a(n) = 7*a(n-1) +65*a(n-2) +1532*a(n-3) +5728*a(n-4) +36988*a(n-5) -79954*a(n-6) -263553*a(n-7) -3722150*a(n-8) +3261200*a(n-9) +8444409*a(n-10) +152666516*a(n-11) -124486119*a(n-12) -492693233*a(n-13) -2755397610*a(n-14) +4009588292*a(n-15) +10293308252*a(n-16) +22336995885*a(n-17) -64924516938*a(n-18) -92755388359*a(n-19) -57474729030*a(n-20) +551610997114*a(n-21) +370469633714*a(n-22) -292081751432*a(n-23) -2630782090265*a(n-24) -301735948456*a(n-25) +2480960089737*a(n-26) +7374666257918*a(n-27) -2515766371859*a(n-28) -7296390671023*a(n-29) -12848715039718*a(n-30) +9261937257065*a(n-31) +11488496485545*a(n-32) +15234546948215*a(n-33) -14912487767600*a(n-34) -11435235548211*a(n-35) -13211824155401*a(n-36) +13970588762093*a(n-37) +7731108650320*a(n-38) +8675779656844*a(n-39) -8276900249091*a(n-40) -3561091877330*a(n-41) -4260429005786*a(n-42) +3209229435553*a(n-43) +1072805871492*a(n-44) +1506322359632*a(n-45) -828404552953*a(n-46) -194259086304*a(n-47) -368735917326*a(n-48) +143996746787*a(n-49) +16734372045*a(n-50) +60312985338*a(n-51) -17012881739*a(n-52) +289141565*a(n-53) -6324998526*a(n-54) +1368060305*a(n-55) -185095968*a(n-56) +399628198*a(n-57) -73289542*a(n-58) +13531943*a(n-59) -13912036*a(n-60) +2336844*a(n-61) -364629*a(n-62) +225419*a(n-63) -31536*a(n-64) +3130*a(n-65) -1258*a(n-66) +110*a(n-67)

A203972 Number of nX5 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

Original entry on oeis.org

13, 396, 16723, 601521, 22100882, 817293052, 30104480870, 1109867821460, 40918040450898, 1508399380147856, 55608018263653107, 2050003686321969840, 75573742529524147667, 2786045396078461420336, 102708210001323641444431
Offset: 1

Views

Author

R. H. Hardin Jan 08 2012

Keywords

Comments

Column 5 of A203975

Examples

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

A203973 Number of n X 6 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

Original entry on oeis.org

24, 1488, 136243, 10443081, 817293052, 64449537503, 5061444598545, 397834775050740, 31270867431167972, 2457732853480046455, 193174081619843169146, 15183059890219083012785, 1193352525118970918791175
Offset: 1

Views

Author

R. H. Hardin, Jan 08 2012

Keywords

Comments

Column 6 of A203975.

Examples

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

Crossrefs

Cf. A203975.

A203968 Number of n X n 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

Original entry on oeis.org

1, 7, 258, 34799, 22100882, 64449537503, 847220834970347, 50681890300309193984, 13775254400039658772386790, 17006093281906665293267116254138
Offset: 1

Views

Author

R. H. Hardin Jan 08 2012

Keywords

Comments

Diagonal of A203975

Examples

			Some solutions for n=4
..0..0..0..0....0..0..1..0....0..0..0..0....0..0..1..0....0..0..1..2
..1..1..0..1....1..1..0..0....0..1..1..1....1..1..0..0....0..0..0..0
..0..0..0..1....0..0..1..2....1..2..0..0....0..1..0..0....0..1..0..1
..1..0..1..0....0..0..0..0....2..0..1..2....0..1..2..1....0..0..0..1
		
Showing 1-7 of 7 results.