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 1-6 of 6 results.

A318539 Number of n X n 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 6, 31, 247, 2905, 46165, 1143583, 41368803, 2165406865, 168220637918, 19176703676628, 3204799103321623, 788247777299643666, 284810105663632654341, 151134158955831615046217
Offset: 1

Views

Author

R. H. Hardin, Aug 28 2018

Keywords

Comments

Diagonal of A318545.

Examples

			Some solutions for n=5
..0..0..0..0..0. .0..0..0..1..0. .0..0..0..0..0. .0..0..0..0..0
..0..0..0..0..0. .1..0..0..0..0. .0..0..1..0..0. .0..0..0..1..0
..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..0
..0..1..0..0..1. .0..1..0..0..0. .0..0..0..0..0. .0..0..0..0..1
..0..0..0..0..0. .0..0..0..1..0. .0..0..0..1..0. .0..0..0..0..0
		

Crossrefs

Cf. A318545.

A318540 Number of nX3 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 3, 6, 13, 26, 52, 107, 218, 442, 899, 1829, 3720, 7565, 15384, 31288, 63632, 129408, 263180, 535236, 1088521, 2213749, 4502149, 9156120, 18621004, 37869943, 77016935, 156631035, 318543977, 647829886, 1317505875, 2679440650, 5449237333
Offset: 1

Views

Author

R. H. Hardin, Aug 28 2018

Keywords

Comments

Column 3 of A318545.

Examples

			Some solutions for n=5
..0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..0
..0..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0. .1..0..0. .1..0..0
..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..1. .0..0..1. .0..0..0
..0..0..1. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..0..1
..0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0
		

Crossrefs

Cf. A318545.

Formula

Empirical: a(n) = a(n-1) +3*a(n-3) +a(n-4) +3*a(n-5) +a(n-7) for n>8

A318541 Number of nX4 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 5, 13, 31, 78, 207, 516, 1288, 3270, 8271, 20866, 52679, 133064, 336062, 848616, 2143101, 5412264, 13667874, 34516655, 87168177, 220132818, 555919912, 1403912579, 3545419471, 8953548234, 22611157039, 57101877461, 144204222586
Offset: 1

Views

Author

R. H. Hardin, Aug 28 2018

Keywords

Comments

Column 4 of A318545.

Examples

			Some solutions for n=5
..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0
..0..0..0..1. .1..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..1..0..0. .1..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..1..0..0
		

Crossrefs

Cf. A318545.

Formula

Empirical: a(n) = a(n-1) +7*a(n-3) +3*a(n-4) +10*a(n-5) -a(n-6) +4*a(n-7) -6*a(n-8) -a(n-9) -a(n-10) -a(n-12) +a(n-13) for n>14

A318542 Number of n X 5 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 8, 26, 78, 247, 784, 2349, 7191, 22268, 68384, 210050, 645832, 1985105, 6102355, 18758291, 57660242, 177244228, 544835790, 1674781291, 5148145759, 15824995614, 48644815851, 149530340549, 459644547764, 1412911535090, 4343179473160
Offset: 1

Views

Author

R. H. Hardin, Aug 28 2018

Keywords

Comments

Column 5 of A318545.

Examples

			Some solutions for n=5
..0..0..0..0..0. .0..0..0..1..0. .0..0..1..0..0. .0..1..0..0..0
..0..0..0..0..0. .1..0..0..0..0. .0..0..0..0..1. .0..0..0..0..0
..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..0..1..0
..1..0..0..0..0. .0..1..0..0..0. .1..0..0..0..0. .0..0..0..0..0
..0..0..0..1..0. .0..0..0..0..0. .0..0..1..0..0. .0..0..0..0..0
		

Crossrefs

Cf. A318545.

Formula

Empirical: a(n) = a(n-1) +14*a(n-3) +7*a(n-4) +33*a(n-5) -6*a(n-6) +20*a(n-7) -48*a(n-8) -4*a(n-9) -32*a(n-10) +30*a(n-12) +14*a(n-13) -8*a(n-14) -10*a(n-15) +9*a(n-16) -3*a(n-17) -13*a(n-18) +9*a(n-19) +7*a(n-20) -5*a(n-21) -a(n-22) +a(n-23) for n>24.

A318543 Number of nX6 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

13, 15, 52, 207, 784, 2905, 10496, 38721, 144148, 531780, 1960675, 7241505, 26745797, 98766587, 364682042, 1346615672, 4972655637, 18362061797, 67803976370, 250374735252, 924538580895, 3413971260050, 12606503235153
Offset: 1

Views

Author

R. H. Hardin, Aug 28 2018

Keywords

Comments

Column 6 of A318545.

Examples

			Some solutions for n=5
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..1..0..0..0..0. .0..0..0..0..0..0
..0..0..0..0..1..0. .0..0..1..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0. .1..0..0..0..0..0
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..1..0..0. .0..0..1..0..0..1
..0..0..0..0..1..0. .0..1..0..0..1..0. .0..0..0..0..0..0. .0..0..0..0..0..0
		

Crossrefs

Cf. A318545.

Formula

Empirical: a(n) = a(n-1) +24*a(n-3) +20*a(n-4) +96*a(n-5) +2*a(n-6) +103*a(n-7) -209*a(n-8) -11*a(n-9) -287*a(n-10) +65*a(n-11) +298*a(n-12) -154*a(n-13) +475*a(n-14) +73*a(n-15) -898*a(n-16) -83*a(n-17) +533*a(n-18) +215*a(n-19) -197*a(n-20) -209*a(n-21) +353*a(n-22) +119*a(n-23) -885*a(n-24) +190*a(n-25) +1077*a(n-26) -441*a(n-27) -760*a(n-28) +403*a(n-29) +336*a(n-30) -210*a(n-31) -91*a(n-32) +66*a(n-33) +14*a(n-34) -12*a(n-35) -a(n-36) +a(n-37) for n>38

A318544 Number of nX7 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

21, 26, 107, 516, 2349, 10496, 46165, 208159, 942764, 4213744, 18870716, 84794983, 380556843, 1707239770, 7660779072, 34376713801, 154258564357, 692193258418, 3106040446532, 13937625995076, 62541652378393, 280640300310752
Offset: 1

Views

Author

R. H. Hardin, Aug 28 2018

Keywords

Comments

Column 7 of A318545.

Examples

			Some solutions for n=5
..0..1..0..0..0..0..0. .0..0..0..0..0..0..0. .0..1..0..0..1..0..0
..0..0..0..0..0..1..0. .0..0..0..0..0..1..0. .0..0..0..0..0..0..0
..0..0..0..0..0..0..0. .0..0..1..0..0..0..0. .0..0..0..0..0..0..0
..0..0..1..0..0..0..0. .0..0..0..0..0..0..1. .1..0..0..0..1..0..0
..0..0..0..0..0..0..0. .0..0..0..1..0..0..0. .0..0..0..0..0..0..0
		

Crossrefs

Cf. A318545.

Formula

Empirical: a(n) = a(n-1) +46*a(n-3) +50*a(n-4) +275*a(n-5) -43*a(n-6) +362*a(n-7) -1637*a(n-8) -271*a(n-9) -3396*a(n-10) +3146*a(n-11) +3432*a(n-12) +6889*a(n-13) +7881*a(n-14) -20207*a(n-15) -21749*a(n-16) +31606*a(n-17) -30087*a(n-18) -43803*a(n-19) +168405*a(n-20) +76348*a(n-21) -293820*a(n-22) -123142*a(n-23) +290600*a(n-24) +147574*a(n-25) -215762*a(n-26) -149500*a(n-27) +261780*a(n-28) +316118*a(n-29) -671671*a(n-30) -764286*a(n-31) +1504462*a(n-32) +1206660*a(n-33) -2414304*a(n-34) -1168911*a(n-35) +2765306*a(n-36) +641957*a(n-37) -2226787*a(n-38) -174104*a(n-39) +1245814*a(n-40) +84501*a(n-41) -498990*a(n-42) -153476*a(n-43) +165047*a(n-44) +149749*a(n-45) -57567*a(n-46) -84000*a(n-47) +18254*a(n-48) +31251*a(n-49) -1064*a(n-50) -8936*a(n-51) -2803*a(n-52) +2260*a(n-53) +1619*a(n-54) -469*a(n-55) -485*a(n-56) +34*a(n-57) +95*a(n-58) +23*a(n-59) -11*a(n-60) -8*a(n-61) +a(n-63) for n>64
Showing 1-6 of 6 results.