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.

A318070 Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 10, 18, 41, 81, 179, 404, 893, 2000, 4516, 10125, 22737, 51181, 115034, 258515, 581380, 1307094, 2938317, 6606445, 14853275, 33392840, 75076165, 168791772, 379483956, 853176349, 1918162541, 4312510121, 9695613622, 21798217755
Offset: 1

Views

Author

R. H. Hardin, Aug 15 2018

Keywords

Comments

Column 3 of A318075.

Examples

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

Crossrefs

Cf. A318075.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -3*a(n-4) -6*a(n-5) +6*a(n-6) for n>10

A318071 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 20, 41, 73, 149, 372, 861, 2016, 4901, 11698, 27986, 67359, 161518, 387556, 930666, 2233451, 5360842, 12868595, 30887501, 74139733, 177960357, 427157604, 1025312853, 2461074852, 5907342192, 14179472548, 34035173339, 81695041734
Offset: 1

Views

Author

R. H. Hardin, Aug 15 2018

Keywords

Comments

Column 4 of A318075.

Examples

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

Crossrefs

Cf. A318075.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -3*a(n-4) -5*a(n-5) -2*a(n-7) +7*a(n-8) -a(n-9) -2*a(n-10) +8*a(n-11) -3*a(n-12) -a(n-13) -3*a(n-14) -3*a(n-15) +4*a(n-16) +a(n-17) -a(n-18) for n>21

A318072 Number of nX5 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 42, 81, 149, 316, 854, 2195, 5752, 15565, 41364, 110930, 299210, 802420, 2158664, 5810654, 15618316, 42022876, 113058411, 304076748, 818075794, 2200737667, 5919964491, 15925927942, 42842509441, 115250505252, 310041060554
Offset: 1

Views

Author

R. H. Hardin, Aug 15 2018

Keywords

Comments

Column 5 of A318075.

Examples

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

Crossrefs

Cf. A318075.

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -16*a(n-4) +16*a(n-5) -27*a(n-6) +15*a(n-7) -6*a(n-8) +4*a(n-9) -3*a(n-10) +29*a(n-11) -9*a(n-12) +17*a(n-13) -7*a(n-14) -11*a(n-15) -13*a(n-16) -7*a(n-17) +5*a(n-18) -7*a(n-19) +a(n-20) +11*a(n-21) -2*a(n-22) +2*a(n-23) +4*a(n-24) -4*a(n-25) +5*a(n-26) -5*a(n-27) -a(n-28) +a(n-29) for n>33

A318073 Number of nX6 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 89, 179, 372, 854, 3029, 9966, 31057, 102906, 339938, 1115341, 3686471, 12202268, 40357737, 133516203, 442017482, 1463416356, 4844264732, 16038582879, 53104714108, 175822278334, 582142483984, 1927505047124, 6381987620459
Offset: 1

Views

Author

R. H. Hardin, Aug 15 2018

Keywords

Comments

Column 6 of A318075.

Examples

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

Crossrefs

Cf. A318075.

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +20*a(n-3) -53*a(n-4) +42*a(n-5) -141*a(n-6) +233*a(n-7) -201*a(n-8) +487*a(n-9) -268*a(n-10) +489*a(n-11) -1197*a(n-12) +587*a(n-13) -2030*a(n-14) +2132*a(n-15) -1266*a(n-16) +2926*a(n-17) -1010*a(n-18) +1350*a(n-19) -2698*a(n-20) +3123*a(n-21) -5723*a(n-22) +5669*a(n-23) -3510*a(n-24) -1261*a(n-25) +1023*a(n-26) +2441*a(n-27) -5509*a(n-28) +9188*a(n-29) -8116*a(n-30) +5375*a(n-31) -2481*a(n-32) +1789*a(n-33) -673*a(n-34) +1170*a(n-35) -4427*a(n-36) +4578*a(n-37) -4241*a(n-38) +2836*a(n-39) -553*a(n-40) -1029*a(n-41) +592*a(n-42) +939*a(n-43) -822*a(n-44) +491*a(n-45) -433*a(n-46) +91*a(n-47) +294*a(n-48) -222*a(n-49) -99*a(n-50) +125*a(n-51) -9*a(n-52) -25*a(n-53) +6*a(n-54) +3*a(n-55) -a(n-56) for n>61

A318074 Number of nX7 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

64, 190, 404, 861, 2195, 9966, 46884, 184156, 819263, 3703730, 15865269, 69944965, 310937380, 1361781447, 5998215467, 26503896368, 116659469704, 513984726015, 2266966511804, 9989194862172, 44021107304800, 194059543279029
Offset: 1

Views

Author

R. H. Hardin, Aug 15 2018

Keywords

Comments

Column 7 of A318075.

Examples

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

Crossrefs

Cf. A318075.

A318069 Number of nXn 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 6, 18, 73, 316, 3029, 46884, 935951, 38183961, 2877277695, 323244675173, 63938089963412, 22744080515948233, 13243562482553493420
Offset: 1

Views

Author

R. H. Hardin, Aug 15 2018

Keywords

Comments

Diagonal of A318075.

Examples

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

Crossrefs

Cf. A318075.
Showing 1-6 of 6 results.