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 11 results. Next

A207264 Number of nX3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

6, 36, 82, 193, 488, 1087, 2305, 4932, 10416, 21716, 45333, 94798, 198291, 415803, 874740, 1845166, 3902324, 8273999, 17581622, 37429453, 79812519, 170419522, 364296166, 779456642, 1669010171, 3575965948, 7665561753, 16438759769
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Column 3 of A207269

Examples

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

Formula

Empirical: a(n) = 5*a(n-1) -9*a(n-2) +12*a(n-3) -22*a(n-4) +25*a(n-5) -16*a(n-6) +21*a(n-7) -17*a(n-8) +a(n-9) -6*a(n-10) +6*a(n-11) +a(n-12) +2*a(n-13) -2*a(n-14) for n>15

A207270 Number of 3Xn 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

6, 36, 82, 217, 499, 1014, 2141, 4188, 8150, 15670, 29517, 55523, 103348, 191593, 353916, 651316, 1196664, 2193747, 4017137, 7347906, 13429145, 24530862, 44784850, 81739060, 149141623, 272067741, 496250336, 905026713, 1650411906
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Row 3 of A207269

Examples

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

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -12*a(n-4) -9*a(n-5) +6*a(n-6) +20*a(n-7) +6*a(n-8) -2*a(n-9) -16*a(n-10) -12*a(n-11) -4*a(n-12) +14*a(n-13) +9*a(n-14) +a(n-15) -6*a(n-16) -2*a(n-17) +a(n-19)

A207263 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 16, 82, 611, 5904, 45520, 467686, 4556171, 48655983, 567847595, 6351729691, 80023297510, 1005050679531, 12834603243934, 174354454607454, 2353308940308585, 32870079608035300, 470039857440029540
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Diagonal of A207269

Examples

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

A207265 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

9, 81, 217, 611, 1910, 5132, 13067, 33937, 86899, 218763, 551672, 1390836, 3491934, 8760137, 21976254, 55062713, 137841712, 344913621, 862466304, 2155128256, 5382374565, 13435295369, 33519373349, 83589288631, 208367881512
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Column 4 of A207269.

Examples

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

Crossrefs

Cf. A207269.

Formula

Empirical: a(n) = 7*a(n-1) -20*a(n-2) +48*a(n-3) -132*a(n-4) +259*a(n-5) -410*a(n-6) +790*a(n-7) -1191*a(n-8) +1369*a(n-9) -2166*a(n-10) +2658*a(n-11) -2175*a(n-12) +3264*a(n-13) -3430*a(n-14) +1780*a(n-15) -3185*a(n-16) +3012*a(n-17) -722*a(n-18) +2246*a(n-19) -1944*a(n-20) -13*a(n-21) -1068*a(n-22) +856*a(n-23) +180*a(n-24) +292*a(n-25) -248*a(n-26) -56*a(n-27) -48*a(n-28) +48*a(n-29) for n>31.

A207266 Number of nX5 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

13, 169, 499, 1602, 5904, 18055, 52240, 156473, 460171, 1324209, 3824481, 11017816, 31464850, 89582619, 254431356, 719347025, 2026808124, 5696170867, 15961932156, 44610315375, 124409802922, 346245984652, 961805475293, 2667346798257
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Column 5 of A207269

Examples

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

Formula

Empirical: a(n) = 8*a(n-1) -27*a(n-2) +82*a(n-3) -276*a(n-4) +660*a(n-5) -1362*a(n-6) +3271*a(n-7) -6143*a(n-8) +9753*a(n-9) -19244*a(n-10) +29834*a(n-11) -37603*a(n-12) +66818*a(n-13) -88111*a(n-14) +87735*a(n-15) -154593*a(n-16) +176242*a(n-17) -132824*a(n-18) +260799*a(n-19) -257210*a(n-20) +131101*a(n-21) -335989*a(n-22) +283983*a(n-23) -71632*a(n-24) +332714*a(n-25) -241037*a(n-26) -2610*a(n-27) -250116*a(n-28) +160089*a(n-29) +38528*a(n-30) +138104*a(n-31) -83144*a(n-32) -32003*a(n-33) -51828*a(n-34) +31992*a(n-35) +13212*a(n-36) +11628*a(n-37) -8424*a(n-38) -2376*a(n-39) -1296*a(n-40) +1296*a(n-41) for n>44

A207267 Number of nX6 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

18, 324, 1014, 3513, 14184, 45520, 135686, 417772, 1253238, 3651096, 10647801, 30923564, 88853464, 254267485, 725590642, 2060214105, 5827339605, 16437397037, 46220378910, 129590864085, 362487844504, 1011664530775, 2817477642474
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Column 6 of A207269

Examples

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

Formula

Empirical: a(n) = 9*a(n-1) -35*a(n-2) +114*a(n-3) -399*a(n-4) +1079*a(n-5) -2463*a(n-6) +6127*a(n-7) -13098*a(n-8) +23694*a(n-9) -47818*a(n-10) +85704*a(n-11) -127793*a(n-12) +223478*a(n-13) -347915*a(n-14) +432707*a(n-15) -690997*a(n-16) +957544*a(n-17) -986264*a(n-18) +1521595*a(n-19) -1906256*a(n-20) +1579613*a(n-21) -2522281*a(n-22) +2871789*a(n-23) -1799626*a(n-24) +3258588*a(n-25) -3358495*a(n-26) +1404974*a(n-27) -3326664*a(n-28) +3084036*a(n-29) -636076*a(n-30) +2678402*a(n-31) -2235957*a(n-32) +8150*a(n-33) -1672281*a(n-34) +1278000*a(n-35) +212203*a(n-36) +777969*a(n-37) -564416*a(n-38) -156032*a(n-39) -251160*a(n-40) +184308*a(n-41) +55008*a(n-42) +50616*a(n-43) -41472*a(n-44) -8208*a(n-45) -5184*a(n-46) +5184*a(n-47) for n>50

A207268 Number of nX7 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

25, 625, 2141, 8327, 38911, 140295, 467686, 1623957, 5467589, 17779942, 57847658, 186862280, 594627012, 1880223340, 5915390781, 18465652946, 57306451587, 177068551553, 544446252694, 1666721759718, 5084288683371, 15456590300469
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Column 7 of A207269

Examples

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

Formula

Empirical: a(n) = 11*a(n-1) -54*a(n-2) +216*a(n-3) -889*a(n-4) +2977*a(n-5) -8510*a(n-6) +25069*a(n-7) -66405*a(n-8) +153594*a(n-9) -368050*a(n-10) +821593*a(n-11) -1609293*a(n-12) +3316946*a(n-13) -6468261*a(n-14) +10971937*a(n-15) -20147157*a(n-16) +35163857*a(n-17) -52207053*a(n-18) +87915951*a(n-19) -139785106*a(n-20) +181957461*a(n-21) -289289211*a(n-22) +424118313*a(n-23) -480420806*a(n-24) +745259282*a(n-25) -1013368615*a(n-26) +980716070*a(n-27) -1545650812*a(n-28) +1947498910*a(n-29) -1558647255*a(n-30) +2631257150*a(n-31) -3050245541*a(n-32) +1912573548*a(n-33) -3721424748*a(n-34) +3923838434*a(n-35) -1753385708*a(n-36) +4394239753*a(n-37) -4162520500*a(n-38) +1086915329*a(n-39) -4318874276*a(n-40) +3645756520*a(n-41) -271419946*a(n-42) +3493357062*a(n-43) -2633648290*a(n-44) -270916251*a(n-45) -2280033769*a(n-46) +1562708364*a(n-47) +395555068*a(n-48) +1165613696*a(n-49) -752684244*a(n-50) -266379104*a(n-51) -446480616*a(n-52) +286392928*a(n-53) +110312752*a(n-54) +119783424*a(n-55) -81864192*a(n-56) -27286272*a(n-57) -20157696*a(n-58) +16008192*a(n-59) +3124224*a(n-60) +1658880*a(n-61) -1658880*a(n-62) for n>65

A207271 Number of 4Xn 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

9, 81, 193, 611, 1602, 3513, 8327, 17568, 36988, 76723, 153865, 308777, 608391, 1189918, 2313136, 4458599, 8562580, 16354499, 31118601, 59018399, 111556847, 210352934, 395641010, 742567333, 1391072247, 2601239676, 4856734666
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Row 4 of A207269

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +5*a(n-2) -a(n-3) -30*a(n-4) -13*a(n-5) +54*a(n-6) +109*a(n-7) -36*a(n-8) -191*a(n-9) -186*a(n-10) +146*a(n-11) +313*a(n-12) +245*a(n-13) -177*a(n-14) -350*a(n-15) -329*a(n-16) +108*a(n-17) +320*a(n-18) +341*a(n-19) -41*a(n-20) -205*a(n-21) -228*a(n-22) -5*a(n-23) +70*a(n-24) +106*a(n-25) +23*a(n-26) -9*a(n-27) -38*a(n-28) -12*a(n-29) +9*a(n-31) +2*a(n-32) -a(n-34)

A207272 Number of 5Xn 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

14, 196, 488, 1910, 5904, 14184, 38911, 90670, 211626, 485438, 1060958, 2325765, 4961769, 10471731, 21898109, 45173720, 92638142, 188237183, 379950333, 762511989, 1520880047, 3019622080, 5966608758, 11740776248, 23016781362
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Row 5 of A207269

Examples

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

Formula

Empirical: a(n) = 3*a(n-1) +5*a(n-2) -5*a(n-3) -55*a(n-4) +a(n-5) +157*a(n-6) +288*a(n-7) -314*a(n-8) -900*a(n-9) -707*a(n-10) +1753*a(n-11) +2735*a(n-12) +1215*a(n-13) -4934*a(n-14) -5958*a(n-15) -2633*a(n-16) +9212*a(n-17) +10737*a(n-18) +6641*a(n-19) -12602*a(n-20) -15845*a(n-21) -13377*a(n-22) +12402*a(n-23) +17826*a(n-24) +20087*a(n-25) -7531*a(n-26) -14262*a(n-27) -22705*a(n-28) +935*a(n-29) +6999*a(n-30) +19219*a(n-31) +3067*a(n-32) -409*a(n-33) -12003*a(n-34) -3358*a(n-35) -2604*a(n-36) +5460*a(n-37) +1873*a(n-38) +2447*a(n-39) -1779*a(n-40) -585*a(n-41) -1256*a(n-42) +396*a(n-43) +61*a(n-44) +422*a(n-45) -53*a(n-46) +23*a(n-47) -96*a(n-48) +3*a(n-49) -9*a(n-50) +14*a(n-51) +a(n-53) -a(n-54)

A207273 Number of 6Xn 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

21, 441, 1087, 5132, 18055, 45520, 140295, 349415, 877101, 2164569, 5025447, 11757247, 26570861, 59370361, 131185317, 285043185, 615447774, 1313196034, 2780365566, 5844983027, 12192162619, 25292923072, 52147005064, 106956186914
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Row 6 of A207269

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +10*a(n-2) +3*a(n-3) -91*a(n-4) -114*a(n-5) +279*a(n-6) +1060*a(n-7) +127*a(n-8) -3605*a(n-9) -6043*a(n-10) +3868*a(n-11) +21907*a(n-12) +21779*a(n-13) -28295*a(n-14) -86016*a(n-15) -61000*a(n-16) +105502*a(n-17) +251602*a(n-18) +159014*a(n-19) -258940*a(n-20) -589991*a(n-21) -403075*a(n-22) +444651*a(n-23) +1134524*a(n-24) +917203*a(n-25) -500154*a(n-26) -1770406*a(n-27) -1742187*a(n-28) +194051*a(n-29) +2177951*a(n-30) +2674848*a(n-31) +564317*a(n-32) -1999418*a(n-33) -3269662*a(n-34) -1515627*a(n-35) +1171675*a(n-36) +3131481*a(n-37) +2150458*a(n-38) -76185*a(n-39) -2282504*a(n-40) -2121528*a(n-41) -729515*a(n-42) +1182231*a(n-43) +1536355*a(n-44) +956874*a(n-45) -338821*a(n-46) -810406*a(n-47) -741228*a(n-48) -55941*a(n-49) +288519*a(n-50) +404337*a(n-51) +126196*a(n-52) -47575*a(n-53) -160958*a(n-54) -77482*a(n-55) -14952*a(n-56) +46223*a(n-57) +29307*a(n-58) +14005*a(n-59) -9038*a(n-60) -7444*a(n-61) -5393*a(n-62) +1011*a(n-63) +1250*a(n-64) +1312*a(n-65) -15*a(n-66) -127*a(n-67) -211*a(n-68) -11*a(n-69) +6*a(n-70) +21*a(n-71) +a(n-72) -a(n-74) for n>75
Showing 1-10 of 11 results. Next