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 13 results. Next

A188868 Number of nX3 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

7, 49, 316, 2032, 13045, 83737, 537496, 3450100, 22145617, 142149013, 912430732, 5856740200, 37593435373, 241305971377, 1548902653984, 9942146967292, 63816977822953, 409630502531629, 2629349654724052, 16877355480293296
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Column 3 of A188874

Examples

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

Formula

Empirical: a(n) = 7*a(n-1) -3*a(n-2) -5*a(n-3) +2*a(n-4)

A188867 Number of n X n binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

2, 16, 316, 21937, 4805140, 3043939392, 6231989402196, 39466951597153578, 765738615267315132042, 46457365071065953602984688, 8729291812408997804314294504336, 5077761520250192263227063403337912870
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Diagonal of A188874

Examples

			Some solutions for 3X3
..1..0..1....0..1..0....0..0..1....0..0..1....0..1..0....1..1..1....1..0..1
..1..1..0....1..0..1....1..1..0....0..1..1....0..1..0....1..0..0....1..1..0
..0..1..0....1..1..0....1..0..0....1..0..0....0..1..1....1..1..1....1..0..0
		

A188869 Number of n X 4 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

13, 169, 1901, 21937, 252932, 2915832, 33617513, 387583973, 4468546833, 51518943080, 593974176396, 6848069915941, 78953031067801, 910268322443949, 10494700553747032, 120995905270195676, 1394990644771317341
Offset: 1

Views

Author

R. H. Hardin, Apr 12 2011

Keywords

Comments

Column 4 of A188874.

Examples

			Some solutions for 3 X 4:
..0..0..1..1....0..1..1..1....0..1..0..0....1..1..1..1....1..0..0..1
..1..1..1..0....0..1..1..1....1..0..1..0....0..0..1..1....1..0..1..1
..1..0..0..1....1..0..1..0....1..0..0..1....1..0..1..1....1..1..1..0
		

Crossrefs

Cf. A188874.

Formula

Empirical: a(n) = 13*a(n-1) -16*a(n-2) -8*a(n-3) -44*a(n-4) +109*a(n-5) -53*a(n-6) +4*a(n-7) for n>8.
Empirical g.f.: x*(13 - 88*x^2 + 32*x^3 + 91*x^4 - 65*x^5 + 17*x^6 - 4*x^7) / (1 - 13*x + 16*x^2 + 8*x^3 + 44*x^4 - 109*x^5 + 53*x^6 - 4*x^7). - Colin Barker, May 01 2018

A188870 Number of n X 5 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

24, 576, 11332, 233756, 4805140, 98892196, 2035428944, 41894114820, 862288002496, 17748103310980, 365301608074080, 7518846739068100, 154757206783943744, 3185301402740998148, 65561696535791184736
Offset: 1

Views

Author

R. H. Hardin, Apr 12 2011

Keywords

Comments

Column 5 of A188874.

Examples

			Some solutions for 3 X 5
..1..0..1..1..0....0..1..0..1..1....1..0..1..1..1....0..1..0..0..1
..0..1..1..0..1....1..1..1..1..0....0..0..1..0..1....0..1..1..1..1
..1..0..1..1..0....1..1..0..1..0....1..1..1..0..0....1..1..1..1..0
		

Crossrefs

Cf. A188874.

Formula

Empirical: a(n) = 24*a(n-1) -67*a(n-2) -48*a(n-3) -540*a(n-4) +2272*a(n-5) +1536*a(n-6) -6944*a(n-7) +2864*a(n-8) +1600*a(n-9) -768*a(n-10) for n>12.

A188871 Number of nX6 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

44, 1936, 65656, 2368612, 84965120, 3043939392, 109002398784, 3903192037184, 139764515932928, 5004636736643072, 179204127483438080, 6416872410001742848, 229772891432953663488, 8227619010998404489216, 294611405650426832932864
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Column 6 of A188874

Examples

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

Formula

Empirical: a(n) = 44*a(n-1) -288*a(n-2) -96*a(n-3) -5152*a(n-4) +62016*a(n-5) +22400*a(n-6) -907712*a(n-7) +671744*a(n-8) +4370432*a(n-9) -5936128*a(n-10) -3608576*a(n-11) +6844416*a(n-12) +393216*a(n-13) -2097152*a(n-14) +262144*a(n-15) for n>17

A188872 Number of nX7 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

81, 6561, 385700, 24609576, 1558668181, 98523889293, 6231989402196, 394199392835388, 24934537275160193, 1577208767277367193, 99764749430808100292, 6310518350640206463960, 399165473341720336437009
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Column 7 of A188874

Examples

			Some solutions for 3X7
..0..1..1..0..1..0..0....0..1..1..0..0..1..1....0..0..1..0..1..0..0
..1..1..1..1..1..0..0....1..0..1..1..0..1..0....0..1..1..0..0..1..0
..1..1..0..0..1..1..1....1..1..1..1..1..1..0....0..0..1..1..0..1..1
		

Formula

Empirical: a(n) = 81*a(n-1) -1148*a(n-2) +2556*a(n-3) -87366*a(n-4) +1804002*a(n-5) -2207080*a(n-6) -70867388*a(n-7) +32972423*a(n-8) +2230665197*a(n-9) -4086729504*a(n-10) -20624987348*a(n-11) +50383243988*a(n-12) +69637220740*a(n-13) -201496189584*a(n-14) -120647252112*a(n-15) +316308674064*a(n-16) +285744226640*a(n-17) -401376039168*a(n-18) -227877410240*a(n-19) +256361762048*a(n-20) +32746840064*a(n-21) -47500075008*a(n-22) +1588264960*a(n-23) +2488795136*a(n-24) -264241152*a(n-25) for n>28

A188873 Number of nX8 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

149, 22201, 2262261, 255014376, 28472229080, 3172528318064, 353870576831949, 39466951597153578, 4401980606077836328, 490982507284484648264, 54762582428023608619232, 6108042623254502635317933
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Column 8 of A188874

Examples

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

Formula

Empirical: a(n) = 149*a(n-1) -4398*a(n-2) +30842*a(n-3) -1071017*a(n-4) +42419902*a(n-5) -186958737*a(n-6) -5487132810*a(n-7) -5756497898*a(n-8) +1087387631361*a(n-9) -3217330567323*a(n-10) -64209634918090*a(n-11) +261184832440296*a(n-12) +1964804773050296*a(n-13) -9055676284180466*a(n-14) -30853023660441496*a(n-15) +126942735337786778*a(n-16) +467179627712906672*a(n-17) -1308654026064782800*a(n-18) -4664912484970429254*a(n-19) +8052344379265931837*a(n-20) +34429207060517608093*a(n-21) -32399664821550333306*a(n-22) -176801014254136744082*a(n-23) +81819087601620852491*a(n-24) +640929053083792727802*a(n-25) -195151072828233886665*a(n-26) -1414404154293905677078*a(n-27) +149569838724183326138*a(n-28) +2209322870544363115221*a(n-29) +117365572103136755839*a(n-30) -2345882783768910142760*a(n-31) -533685002438687208272*a(n-32) +1928449256658597805216*a(n-33) +378229639264198628608*a(n-34) -949690813888396558336*a(n-35) -262558184049887631616*a(n-36) +430728124483681647616*a(n-37) +24336441887762870272*a(n-38) -106340390672831414272*a(n-39) -2414110705106059264*a(n-40) +32031048273768808448*a(n-41) -9751294909259710464*a(n-42) -1966300493975912448*a(n-43) +1204649769205497856*a(n-44) +148027361663647744*a(n-45) -163273365769945088*a(n-46) +31325723004239872*a(n-47) -2150730643275776*a(n-48) +50182397886464*a(n-49) -274877906944*a(n-50) for n>53

A188875 Number of 3Xn binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

8, 64, 316, 1901, 11332, 65656, 385700, 2262261, 13249261, 77665756, 455194656, 2667688716, 15634970127, 91633239536, 537041598796, 3147488927460, 18446758005813, 108112489924349, 633624215112740, 3713535944800748
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Row 3 of A188874

Examples

			Some solutions for 3X3
..1..1..0....1..1..1....0..1..1....1..1..1....0..1..1....0..1..1....0..0..1
..1..0..0....1..0..0....1..0..0....1..0..1....0..1..1....1..1..1....0..1..0
..1..1..0....1..1..1....1..0..1....0..0..1....1..1..0....1..1..1....1..0..1
		

Formula

Empirical: a(n) = 3*a(n-1) +10*a(n-2) +41*a(n-3) -3*a(n-4) -10*a(n-5) -124*a(n-6) +96*a(n-7) -50*a(n-8) +71*a(n-9) -43*a(n-10) +14*a(n-11) -5*a(n-12) +a(n-13)

A188876 Number of 4Xn binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

16, 256, 2032, 21937, 233756, 2368612, 24609576, 255014376, 2634386061, 27264641304, 282086403837, 2918043746684, 30189606384325, 312327215078591, 3231163537843117, 33428102017481312, 345830567133874557
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Row 4 of A188874

Examples

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

Formula

Empirical: a(n) = a(n-1) +35*a(n-2) +489*a(n-3) +1430*a(n-4) +3210*a(n-5) -16936*a(n-6) -34960*a(n-7) -129709*a(n-8) +447659*a(n-9) -9285*a(n-10) +2398289*a(n-11) -7764277*a(n-12) +9817767*a(n-13) -30901833*a(n-14) +73765373*a(n-15) -103959405*a(n-16) +191812683*a(n-17) -341437562*a(n-18) +425552930*a(n-19) -569154650*a(n-20) +783877862*a(n-21) -816100061*a(n-22) +828497121*a(n-23) -897239562*a(n-24) +761960822*a(n-25) -589246249*a(n-26) +509146937*a(n-27) -353900338*a(n-28) +211843142*a(n-29) -155156946*a(n-30) +92575238*a(n-31) -42848915*a(n-32) +27269921*a(n-33) -14401825*a(n-34) +5088049*a(n-35) -2893419*a(n-36) +1356573*a(n-37) -340325*a(n-38) +190245*a(n-39) -80371*a(n-40) +11185*a(n-41) -7600*a(n-42) +3260*a(n-43) -162*a(n-44) +154*a(n-45) -81*a(n-46) +a(n-47) -a(n-48) +a(n-49)

A188877 Number of 5Xn binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

Original entry on oeis.org

32, 1024, 13045, 252932, 4805140, 84965120, 1558668181, 28472229080, 517776315573, 9442392487092, 172104527985533, 3136183930249272, 57160501361811036, 1041761230924349515, 18986128724688300231
Offset: 1

Views

Author

R. H. Hardin Apr 12 2011

Keywords

Comments

Row 5 of A188874

Examples

			Some solutions for 5X3
..0..0..1....1..0..0....1..1..1....0..0..1....0..1..1....1..0..1....0..1..1
..0..1..0....0..1..0....1..0..1....1..0..0....1..1..1....1..0..1....1..1..0
..1..0..1....0..1..1....1..1..1....0..1..1....1..1..1....1..0..0....0..0..1
..1..0..1....0..1..0....1..0..0....1..0..1....1..0..0....1..1..0....1..0..0
..1..1..0....1..0..1....0..1..1....0..0..1....0..1..1....0..1..1....1..0..1
		
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