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 10 results.

A207763 Number of 3Xn 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

6, 36, 82, 221, 493, 1095, 2654, 6203, 14182, 33242, 77781, 180207, 419683, 979186, 2277663, 5301348, 12351370, 28755901, 66942929, 155895195, 362997882, 845159395, 1967953186, 4582333234, 10669471213, 24843252803, 57846384111
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 3 of A207762

Examples

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

Formula

Empirical: a(n) = a(n-1) +8*a(n-3) +a(n-5) -12*a(n-6) -3*a(n-7) +a(n-8) +10*a(n-9) -2*a(n-10) -3*a(n-12) for n>14

A207757 Number of n X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 16, 82, 663, 6552, 56651, 887114, 17141340, 265932767, 7838599272, 322656587622, 9334787856534, 545237703029106, 50069011902134767, 2724265960028933880, 333854434181630056441, 70233064417444890074531
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Diagonal of A207762

Examples

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

A207758 Number of nX4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

9, 81, 221, 663, 2245, 6459, 17563, 48649, 131269, 344873, 902075, 2342619, 6021103, 15395621, 39219821, 99470227, 251449497, 634148313, 1595707571, 4007571389, 10049914241, 25169768531, 62965428327, 157368593823, 392995561393
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Column 4 of A207762

Examples

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

Formula

Empirical: a(n) = 6*a(n-1) -14*a(n-2) +30*a(n-3) -77*a(n-4) +120*a(n-5) -153*a(n-6) +281*a(n-7) -311*a(n-8) +236*a(n-9) -422*a(n-10) +351*a(n-11) -110*a(n-12) +387*a(n-13) -284*a(n-14) -3*a(n-15) -264*a(n-16) +172*a(n-17) +52*a(n-18) +84*a(n-19) -56*a(n-20) -24*a(n-21) -16*a(n-22) +16*a(n-23) for n>24

A207759 Number of nX5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

13, 169, 493, 1664, 6552, 21547, 67330, 217902, 687672, 2108870, 6459569, 19653779, 59068262, 176517135, 525307673, 1554420841, 4579979219, 13453583712, 39397940890, 115063670433, 335345658200, 975522972020, 2833090734366
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Column 5 of A207762

Examples

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

Formula

Empirical: a(n) = 7*a(n-1) -18*a(n-2) +42*a(n-3) -135*a(n-4) +245*a(n-5) -331*a(n-6) +828*a(n-7) -1162*a(n-8) +899*a(n-9) -2506*a(n-10) +2983*a(n-11) -933*a(n-12) +5079*a(n-13) -5361*a(n-14) -397*a(n-15) -7067*a(n-16) +6470*a(n-17) +2910*a(n-18) +6260*a(n-19) -5476*a(n-20) -3504*a(n-21) -3776*a(n-22) +3472*a(n-23) +1984*a(n-24) +1120*a(n-25) -1184*a(n-26) -576*a(n-27) -128*a(n-28) +256*a(n-29) for n>31

A207760 Number of nX6 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

19, 361, 1095, 4018, 16920, 56651, 178627, 581166, 1838374, 5659448, 17426525, 53447015, 162579914, 493375310, 1495959569, 4527344211, 13690772759, 41408994328, 125273246604, 379174015659, 1148704163123, 3483663286586
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Column 6 of A207762

Examples

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

Formula

Empirical: a(n) = 8*a(n-1) -23*a(n-2) +57*a(n-3) -207*a(n-4) +422*a(n-5) -606*a(n-6) +1791*a(n-7) -2780*a(n-8) +2105*a(n-9) -7999*a(n-10) +9553*a(n-11) -1014*a(n-12) +25158*a(n-13) -21379*a(n-14) -11660*a(n-15) -61601*a(n-16) +31255*a(n-17) +40719*a(n-18) +108770*a(n-19) -27506*a(n-20) -67135*a(n-21) -133892*a(n-22) +17047*a(n-23) +63911*a(n-24) +107159*a(n-25) -9874*a(n-26) -38230*a(n-27) -51716*a(n-28) +8820*a(n-29) +12304*a(n-30) +14080*a(n-31) -5424*a(n-32) -2368*a(n-33) -1376*a(n-34) +1696*a(n-35) +64*a(n-36) +128*a(n-37) -256*a(n-38) for n>41

A207761 Number of nX7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

28, 784, 2654, 11509, 59252, 235872, 887114, 3488718, 13324700, 49528948, 184808314, 687726602, 2538842648, 9356257550, 34457742152, 126613738962, 464595415916, 1703705288482, 6242056357676, 22851249560906, 83609513888316
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Column 7 of A207762

Examples

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

Formula

Empirical: a(n) = 9*a(n-1) -30*a(n-2) +101*a(n-3) -452*a(n-4) +1080*a(n-5) -2212*a(n-6) +7988*a(n-7) -14310*a(n-8) +18574*a(n-9) -74548*a(n-10) +97674*a(n-11) -59812*a(n-12) +477460*a(n-13) -408258*a(n-14) -76060*a(n-15) -2426098*a(n-16) +1052702*a(n-17) +1527766*a(n-18) +9776968*a(n-19) -978888*a(n-20) -7207648*a(n-21) -30286394*a(n-22) -3635038*a(n-23) +19889764*a(n-24) +70635534*a(n-25) +17114220*a(n-26) -37149004*a(n-27) -121787501*a(n-28) -35300157*a(n-29) +49526360*a(n-30) +154324589*a(n-31) +41825606*a(n-32) -49157144*a(n-33) -142598668*a(n-34) -27479092*a(n-35) +38216016*a(n-36) +96382504*a(n-37) +4500656*a(n-38) -23708240*a(n-39) -48440992*a(n-40) +7538688*a(n-41) +11797440*a(n-42) +18533248*a(n-43) -7068544*a(n-44) -3979392*a(n-45) -5485568*a(n-46) +3083776*a(n-47) +727552*a(n-48) +1075712*a(n-49) -813056*a(n-50) -5120*a(n-51) -122880*a(n-52) +161792*a(n-53) -20480*a(n-54) +8192*a(n-55) -16384*a(n-56) for n>60

A207764 Number of 4Xn 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

9, 81, 193, 663, 1664, 4018, 11509, 30943, 79178, 213444, 574517, 1510235, 4016905, 10742833, 28499913, 75702647, 201719465, 536397481, 1425655190, 3793651190, 10091485607, 26833849671, 71376964346, 189863830540, 504956635718
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 4 of A207762

Examples

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

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +15*a(n-3) -28*a(n-4) +16*a(n-5) -51*a(n-6) +83*a(n-7) -21*a(n-8) +65*a(n-9) -150*a(n-10) +64*a(n-11) -54*a(n-12) +132*a(n-13) -76*a(n-14) +26*a(n-15) -40*a(n-16) +20*a(n-17) for n>19

A207765 Number of 5Xn 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

14, 196, 488, 2245, 6552, 16920, 59252, 188350, 538950, 1709438, 5427808, 16323968, 50456976, 158170514, 485197851, 1494251065, 4644507594, 14337420385, 44204714925, 136866164125, 423105979612, 1306174738721, 4038464232068
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 5 of A207762

Examples

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

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +28*a(n-3) -56*a(n-4) +35*a(n-5) -225*a(n-6) +391*a(n-7) -137*a(n-8) +850*a(n-9) -1626*a(n-10) +593*a(n-11) -1884*a(n-12) +4000*a(n-13) -1860*a(n-14) +2560*a(n-15) -5448*a(n-16) +2844*a(n-17) -1904*a(n-18) +3760*a(n-19) -1984*a(n-20) +576*a(n-21) -1024*a(n-22) +512*a(n-23) for n>25

A207766 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

21, 441, 1087, 6459, 21547, 56651, 235872, 862146, 2629798, 9529570, 34708948, 114255562, 396908066, 1416972222, 4828733870, 16634895736, 58487207221, 201993811973, 696619145912, 2429011369708, 8423471768055, 29119549204363
Offset: 1

Views

Author

R. H. Hardin, Feb 19 2012

Keywords

Comments

Row 6 of A207762.

Examples

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

Crossrefs

Cf. A207762.

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +47*a(n-3) -100*a(n-4) +68*a(n-5) -729*a(n-6) +1351*a(n-7) -599*a(n-8) +5751*a(n-9) -10798*a(n-10) +4250*a(n-11) -27354*a(n-12) +54520*a(n-13) -24176*a(n-14) +83574*a(n-15) -172480*a(n-16) +85820*a(n-17) -163088*a(n-18) +335152*a(n-19) -176096*a(n-20) +192808*a(n-21) -384288*a(n-22) +203280*a(n-23) -123648*a(n-24) +236544*a(n-25) -122496*a(n-26) +32640*a(n-27) -59904*a(n-28) +29952*a(n-29) for n>31.

A207767 Number of 7Xn 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

31, 961, 2305, 17563, 67330, 178627, 887114, 3733566, 11979209, 49800326, 208738438, 742476229, 2900533473, 11843654162, 44397947317, 170655647841, 681016789541, 2614418854083, 10044216333681, 39503065976101
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Row 7 of A207762

Examples

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

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +75*a(n-3) -165*a(n-4) +117*a(n-5) -1993*a(n-6) +3819*a(n-7) -1872*a(n-8) +28120*a(n-9) -52719*a(n-10) +21633*a(n-11) -245836*a(n-12) +475386*a(n-13) -202047*a(n-14) +1424731*a(n-15) -2854572*a(n-16) +1336596*a(n-17) -5595456*a(n-18) +11419032*a(n-19) -5756664*a(n-20) +14788744*a(n-21) -30146304*a(n-22) +15765936*a(n-23) -25534368*a(n-24) +51292992*a(n-25) -27030768*a(n-26) +27214704*a(n-27) -53527680*a(n-28) +27914688*a(n-29) -16039296*a(n-30) +30855168*a(n-31) -15780096*a(n-32) +3960576*a(n-33) -7464960*a(n-34) +3732480*a(n-35) for n>37
Showing 1-10 of 10 results.