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.

A188768 Number of nX3 binary arrays without the pattern 0 1 0 vertically or horizontally.

Original entry on oeis.org

7, 49, 240, 1103, 5357, 26564, 130828, 641137, 3143331, 15426387, 75714198, 371548402, 1823195326, 8946675170, 43903164079, 215441286043, 1057208843688, 5187912250379, 25458023997998, 124927142385391, 613040099740828
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 3 of A188774

Examples

			Some solutions for 4X3
..1..0..1....0..1..1....1..0..1....1..1..1....1..1..0....0..0..1....1..1..0
..1..0..1....1..0..1....1..0..0....1..0..0....0..0..1....0..0..0....1..1..1
..1..0..1....1..0..0....0..0..0....0..0..1....0..0..1....1..1..0....1..0..1
..0..0..0....1..1..0....1..0..0....0..1..1....1..0..0....1..1..1....1..1..0
		

Formula

Empirical: a(n) = 5*a(n-1) -6*a(n-2) +23*a(n-3) +18*a(n-4) +5*a(n-5) +49*a(n-6) -30*a(n-7) -87*a(n-8) -6*a(n-9) +19*a(n-10) +8*a(n-11) +5*a(n-12) -a(n-13) -a(n-14)

A188769 Number of nX4 binary arrays without the pattern 0 1 0 vertically or horizontally.

Original entry on oeis.org

12, 144, 1103, 7868, 60215, 471349, 3658041, 28240356, 218167554, 1687182731, 13048449716, 100897161709, 780153946407, 6032429478257, 46645504480302, 360683651186398, 2788957182000107, 21565381169985048, 166752620658425497
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 4 of A188774

Examples

			Some solutions for 3X4
..1..0..0..0....0..0..1..1....0..1..1..1....0..1..1..1....1..1..0..0
..1..0..0..0....0..0..0..0....0..0..1..1....1..0..0..0....1..0..0..0
..0..0..0..0....0..0..0..1....0..1..1..1....1..0..1..1....1..1..1..0
		

Formula

Empirical: a(n) = 9*a(n-1) -26*a(n-2) +120*a(n-3) +55*a(n-4) -207*a(n-5) +1143*a(n-6) -2223*a(n-7) -7821*a(n-8) +5631*a(n-9) +15011*a(n-10) +4093*a(n-11) -1011*a(n-12) -14644*a(n-13) -19696*a(n-14) -2087*a(n-15) +2890*a(n-16) +11655*a(n-17) +9364*a(n-18) +4150*a(n-19) +1661*a(n-20) -896*a(n-21) -501*a(n-22) -175*a(n-23) -82*a(n-24) +24*a(n-25) +12*a(n-26)

A188770 Number of nX5 binary arrays without the pattern 0 1 0 vertically or horizontally.

Original entry on oeis.org

21, 441, 5357, 60215, 738031, 9260851, 114928827, 1418719059, 17534258973, 216934553467, 2683742012463, 33195135531017, 410584897617051, 5078597128434733, 62818418192287393, 777013463038269315
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 5 of A188774

Examples

			Some solutions for 3X5
..1..1..0..1..1....1..1..1..1..1....1..1..0..0..0....1..0..1..1..0
..0..1..1..0..1....1..0..1..1..1....1..0..0..0..0....1..0..1..1..0
..1..1..1..1..0....1..0..0..1..1....1..1..1..0..1....0..0..0..0..1
		

Formula

Empirical: a(n) = 12*a(n-1) -34*a(n-2) +349*a(n-3) +1777*a(n-4) -2954*a(n-5) +16428*a(n-6) -50372*a(n-7) -826452*a(n-8) -284808*a(n-9) +2677029*a(n-10) +7103943*a(n-11) +84848429*a(n-12) +92733632*a(n-13) -704130678*a(n-14) -1408367121*a(n-15) -170953276*a(n-16) +2530631860*a(n-17) +15426821098*a(n-18) +26026362695*a(n-19) -10562390615*a(n-20) -63303657046*a(n-21) -186442796778*a(n-22) -294709147635*a(n-23) +52891360993*a(n-24) +470509771394*a(n-25) +1401923559917*a(n-26) +2366816377369*a(n-27) +847969028551*a(n-28) -236781572071*a(n-29) -5197208853480*a(n-30) -9799362882578*a(n-31) -8117532389762*a(n-32) -11659304320720*a(n-33) +2726011701444*a(n-34) +4079145059625*a(n-35) +12257366411312*a(n-36) +15768165034291*a(n-37) +2100988995383*a(n-38) +5307745327989*a(n-39) -9786415785169*a(n-40) -7875869693149*a(n-41) -3846427592880*a(n-42) -5445730695613*a(n-43) +4410839511443*a(n-44) +1545211814877*a(n-45) +1949821109517*a(n-46) +1917312603154*a(n-47) -1325513042612*a(n-48) -154693016638*a(n-49) -407142438623*a(n-50) -368447878313*a(n-51) +291082101634*a(n-52) +31398804662*a(n-53) +22130829827*a(n-54) +40030081560*a(n-55) -37025725802*a(n-56) -6898111152*a(n-57) +4080211514*a(n-58) -1734054000*a(n-59) +1712530236*a(n-60) +550479816*a(n-61) -445020240*a(n-62) -11156224*a(n-63) +9983040*a(n-64) -10775392*a(n-65) +6661280*a(n-66) +980928*a(n-67) -544448*a(n-68) +43968*a(n-69) -23040*a(n-70) -6912*a(n-71) +3072*a(n-72)

A188771 Number of nX6 binary arrays without the pattern 0 1 0 vertically or horizontally.

Original entry on oeis.org

37, 1369, 26564, 471349, 9260851, 186969392, 3725504150, 73772281769, 1462969839335, 29048017912245, 576713868595398, 11447410876473182, 227220607547197774, 4510286415908468400, 89529020198750399977
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 6 of A188774

Examples

			Some solutions for 3X6
..1..0..1..1..1..1....0..0..0..1..1..1....1..1..1..1..0..0....1..1..1..0..0..0
..1..1..1..1..0..0....0..1..1..1..1..1....1..1..1..1..1..0....1..0..0..1..1..0
..0..1..1..1..1..0....1..1..1..1..1..1....0..0..0..0..1..1....1..1..0..1..1..0
		

A188772 Number of n X 7 binary arrays without the pattern 0 1 0 vertically or horizontally.

Original entry on oeis.org

65, 4225, 130828, 3658041, 114928827, 3725504150, 118984786902, 3772804871287, 119816916752612, 3810670337663147, 121188283006836223, 3853067582126261844, 122500758733139379893, 3894834135997239917934, 123835414312916823578527
Offset: 1

Views

Author

R. H. Hardin, Apr 09 2011

Keywords

Comments

Column 7 of A188774.

Examples

			Some solutions for 3 X 7
..1..0..0..1..1..0..1....1..1..0..0..0..0..0....1..1..0..0..0..1..1
..0..0..0..1..1..0..0....1..0..1..1..1..0..0....1..1..0..1..1..0..1
..0..0..0..0..0..0..1....1..0..1..1..1..1..0....0..1..1..1..1..0..1
		

Crossrefs

Cf. A188774.

A188773 Number of nX8 binary arrays without the pattern 0 1 0 vertically or horizontally.

Original entry on oeis.org

114, 12996, 641137, 28240356, 1418719059, 73772281769, 3772804871287, 191430611504482, 9730213136489790, 495351189671153051, 25215983801380475678, 1283271380583388569167, 65304983732786290676835
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 8 of A188774

Examples

			Some solutions for 3X8
..0..0..1..1..0..1..1..1....0..0..0..1..1..0..0..0....0..0..0..0..0..0..0..1
..1..1..1..0..0..0..0..1....0..1..1..1..1..1..0..0....0..0..1..1..0..1..1..0
..1..1..1..1..0..1..1..0....1..1..1..0..1..1..1..0....1..0..1..1..0..1..1..1
		

A188767 Number of n X n binary arrays without the pattern 0 1 0 vertically or horizontally.

Original entry on oeis.org

2, 16, 240, 7868, 738031, 186969392, 118984786902, 191430611504482, 791786310866344064, 8423565813650647334361, 229714505025192315490199222, 16049804227721101224353628972128
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Diagonal of A188774

Examples

			Some solutions for 3X3
..1..1..1....1..0..1....1..1..0....1..1..1....0..1..1....0..1..1....1..1..1
..0..1..1....1..1..1....1..1..0....0..1..1....1..1..1....0..0..1....0..0..0
..1..1..1....1..1..0....1..0..0....0..0..1....1..0..1....0..0..0....1..0..0
		
Showing 1-7 of 7 results.