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 1-8 of 8 results.

A203084 Number of (n+2) X 3 binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

98, 253, 621, 1575, 4000, 10057, 25384, 64140, 161819, 408415, 1031041, 2602296, 6568305, 16579362, 41847510, 105626421, 266611217, 672949667, 1698582936, 4287374163, 10821707646, 27314936026, 68945297129, 174023973205
Offset: 1

Views

Author

R. H. Hardin, Dec 29 2011

Keywords

Comments

Column 1 of A203091.

Examples

			Some solutions for n=3:
  1 0 0    1 1 0    1 1 0    0 1 0    0 0 1    1 1 1    1 0 0
  1 1 0    1 1 0    1 1 1    1 0 0    1 1 1    1 1 0    1 1 0
  1 1 1    1 1 1    1 1 1    0 0 1    1 0 0    1 1 0    0 1 1
  1 1 1    0 1 1    1 1 1    0 1 1    1 0 0    0 1 1    0 1 1
  0 1 0    0 0 1    0 1 0    1 1 0    0 1 1    0 0 1    1 0 0
		

Crossrefs

Cf. A203091.

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 6*a(n-3) + 2*a(n-4) + 3*a(n-5) - a(n-6) - a(n-8) - a(n-9) - a(n-10).
Empirical g.f.: x*(98 + 155*x + 270*x^2 + 113*x^3 + 90*x^4 - 44*x^5 - 26*x^6 - 61*x^7 - 53*x^8 - 36*x^9) / (1 - x - x^2 - 6*x^3 - 2*x^4 - 3*x^5 + x^6 + x^8 + x^9 + x^10). - Colin Barker, Mar 03 2018

A203085 Number of (n+2)X4 binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

253, 787, 2237, 6615, 19723, 57699, 169561, 500813, 1473813, 4336509, 12776787, 37624405, 110768047, 326202095, 960592477, 2828495527, 8329036847, 24526561909, 72221962493, 212669436487, 626242809531, 1844074518231
Offset: 1

Views

Author

R. H. Hardin Dec 29 2011

Keywords

Comments

Column 2 of A203091

Examples

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-2) +10*a(n-3) +6*a(n-4) -5*a(n-5) -10*a(n-6) -8*a(n-7) +2*a(n-8) +10*a(n-9) -24*a(n-10) -20*a(n-11) +23*a(n-12) +22*a(n-13) -10*a(n-14)

A203086 Number of (n+2)X5 binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

621, 2237, 7558, 26528, 92748, 319956, 1110338, 3857116, 13368366, 46374172, 160928422, 558198034, 1936342232, 6717789912, 23304299530, 80843139172, 280454591492, 972921980908, 3375134923804, 11708636231942, 40618271541636
Offset: 1

Views

Author

R. H. Hardin Dec 29 2011

Keywords

Comments

Column 3 of A203091

Examples

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-2) +19*a(n-3) +17*a(n-4) +5*a(n-5) -57*a(n-6) -51*a(n-7) +48*a(n-8) +197*a(n-9) -63*a(n-10) -429*a(n-11) -144*a(n-12) +443*a(n-13) +246*a(n-14) -220*a(n-15) -81*a(n-16) +58*a(n-17) -65*a(n-18) +10*a(n-19) +49*a(n-20) +20*a(n-21) +20*a(n-22) for n>24

A203087 Number of (n+2)X6 binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

1575, 6615, 26528, 112334, 470807, 1946072, 8108104, 33749405, 140139039, 582872782, 2424232694, 10076881075, 41899814371, 174230232505, 724397027179, 3011944328140, 12523598001417, 52071590286001, 216507575162589
Offset: 1

Views

Author

R. H. Hardin Dec 29 2011

Keywords

Comments

Column 4 of A203091

Examples

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

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +34*a(n-3) +40*a(n-4) -31*a(n-5) -224*a(n-6) -413*a(n-7) +433*a(n-8) +1505*a(n-9) +703*a(n-10) -2455*a(n-11) -5056*a(n-12) +2075*a(n-13) +4934*a(n-14) -656*a(n-15) +3696*a(n-16) +18044*a(n-17) -16513*a(n-18) -39362*a(n-19) +8986*a(n-20) +39868*a(n-21) -19137*a(n-22) +10671*a(n-23) +7513*a(n-24) -14687*a(n-25) -4882*a(n-26) -718*a(n-27) +4632*a(n-28) +3198*a(n-29) +2571*a(n-30) +1542*a(n-31) -1549*a(n-32) +249*a(n-33) -84*a(n-34) -330*a(n-35) +54*a(n-36) -216*a(n-37) for n>41

A203088 Number of (n+2)X7 binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

4000, 19723, 92748, 470807, 2370796, 11699349, 58260775, 290231774, 1440610700, 7161014248, 35609572095, 176960438476, 879584805301, 4372483391637, 21733245679944, 108026928008832, 536972664561780, 2669084720571895
Offset: 1

Views

Author

R. H. Hardin Dec 29 2011

Keywords

Comments

Column 5 of A203091

Examples

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

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +67*a(n-3) +95*a(n-4) +39*a(n-5) -787*a(n-6) -1996*a(n-7) -1419*a(n-8) +6228*a(n-9) +16781*a(n-10) +27340*a(n-11) -22505*a(n-12) -163643*a(n-13) -232318*a(n-14) -44611*a(n-15) +756933*a(n-16) +2255098*a(n-17) +1234664*a(n-18) -6024326*a(n-19) -8760446*a(n-20) +2608178*a(n-21) +13003422*a(n-22) +7775870*a(n-23) +4006698*a(n-24) -6086060*a(n-25) -18623318*a(n-26) -8885831*a(n-27) -10620166*a(n-28) +3421476*a(n-29) +36056453*a(n-30) +14043377*a(n-31) -391762*a(n-32) -5237906*a(n-33) -27563307*a(n-34) +19864148*a(n-35) +14011332*a(n-36) -2031690*a(n-37) -2983530*a(n-38) -42780677*a(n-39) -8866305*a(n-40) -12102979*a(n-41) +6725362*a(n-42) +6269863*a(n-43) +192462*a(n-44) +1886386*a(n-45) -1148964*a(n-46) +351634*a(n-47) +84728*a(n-48) -135432*a(n-49) +66240*a(n-50) -11392*a(n-51) for n>57

A203089 Number of (n+2)X8 binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

10057, 57699, 319956, 1946072, 11699349, 68989536, 411159715, 2448491999, 14527671131, 86335466624, 513171415313, 3048439984301, 18113248802206, 107631805106769, 639499854727113, 3799762632265266, 22577634198427404
Offset: 1

Views

Author

R. H. Hardin Dec 29 2011

Keywords

Comments

Column 6 of A203091

Examples

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

Formula

Empirical: a(n) = a(n-1) +10*a(n-2) +114*a(n-3) +194*a(n-4) -374*a(n-5) -3394*a(n-6) -9222*a(n-7) +3450*a(n-8) +63642*a(n-9) +184963*a(n-10) +133901*a(n-11) -670343*a(n-12) -2882799*a(n-13) -4475403*a(n-14) +3008747*a(n-15) +24197011*a(n-16) +91798704*a(n-17) +121068474*a(n-18) -390320614*a(n-19) -1585027827*a(n-20) -174789262*a(n-21) +5714123205*a(n-22) +6261482640*a(n-23) -7713853231*a(n-24) -16454030340*a(n-25) -8192162679*a(n-26) +1798821063*a(n-27) +25115593177*a(n-28) +67177230424*a(n-29) +35073379023*a(n-30) -39396358499*a(n-31) -204500017334*a(n-32) -287221302594*a(n-33) +121869444771*a(n-34) +651630500775*a(n-35) +404642219492*a(n-36) +228946678981*a(n-37) -1264088589328*a(n-38) -1430803465320*a(n-39) +390503342575*a(n-40) +473447922911*a(n-41) +2967943964011*a(n-42) +918369676941*a(n-43) -1966816449977*a(n-44) -927546061788*a(n-45) -4437543138631*a(n-46) +1189531776710*a(n-47) +1897734679450*a(n-48) +1634774070437*a(n-49) +4332697240293*a(n-50) -3798066275331*a(n-51) -714550711465*a(n-52) -4667088307373*a(n-53) -2144516247817*a(n-54) +2343538410003*a(n-55) +1252001226637*a(n-56) +5873078981680*a(n-57) +2212331507462*a(n-58) +2397332943541*a(n-59) +585948017993*a(n-60) -931286828763*a(n-61) -337232767617*a(n-62) -995783593576*a(n-63) -245594595326*a(n-64) -137014489737*a(n-65) -65506443688*a(n-66) +91651098269*a(n-67) -29737584906*a(n-68) -3191357778*a(n-69) -8285725970*a(n-70) -20928028142*a(n-71) +5723741150*a(n-72) +5048689705*a(n-73) +1215517273*a(n-74) +4795269673*a(n-75) -426942656*a(n-76) -796654841*a(n-77) +348187379*a(n-78) -367811289*a(n-79) +49871525*a(n-80) +110312488*a(n-81) -19031169*a(n-82) +9039685*a(n-83) +1655848*a(n-84) -4085144*a(n-85) +285268*a(n-86) +414624*a(n-87) +144*a(n-88) for n>96

A203090 Number of (n+2)X9 binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

25384, 169561, 1110338, 8108104, 58260775, 411159715, 2942039652, 21001045294, 149307714269, 1063928895151, 7580777433365, 53974528946958, 384438447373736, 2738313728520726, 19501965156958738, 138898967881687747
Offset: 1

Views

Author

R. H. Hardin Dec 29 2011

Keywords

Comments

Column 7 of A203091

Examples

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

A203083 Number of (n+2)X(n+2) binary arrays avoiding patterns 000 and 101 in rows and columns.

Original entry on oeis.org

98, 787, 7558, 112334, 2370796, 68989536, 2942039652, 179655879540, 15600032557062, 1955530152142929, 351771423028876126, 90632490221136217305
Offset: 1

Views

Author

R. H. Hardin Dec 29 2011

Keywords

Comments

Diagonal of A203091

Examples

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