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 1-5 of 5 results.

A221663 Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 nX2 array.

Original entry on oeis.org

2, 12, 48, 256, 856, 4096, 15872, 65344, 259584, 1048576, 4177632, 16777216, 67051520, 268430336, 1073479680, 4294967296, 17178580480, 68719476736, 274872664064, 1099511513088, 4398023442432, 17592186044416, 70368641459200
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Column 2 of A221666

Examples

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

Formula

Empirical: a(n) = 4*a(n-1) +8*a(n-2) -32*a(n-3) -16*a(n-4) +64*a(n-5) +52*a(n-6) -208*a(n-7) -416*a(n-8) +1664*a(n-9) +832*a(n-10) -3328*a(n-11) -1056*a(n-12) +4224*a(n-13) +8448*a(n-14) -33792*a(n-15) -16896*a(n-16) +67584*a(n-17) +10880*a(n-18) -43520*a(n-19) -87040*a(n-20) +348160*a(n-21) +174080*a(n-22) -696320*a(n-23) -62720*a(n-24) +250880*a(n-25) +501760*a(n-26) -2007040*a(n-27) -1003520*a(n-28) +4014080*a(n-29) +205824*a(n-30) -823296*a(n-31) -1646592*a(n-32) +6586368*a(n-33) +3293184*a(n-34) -13172736*a(n-35) -360448*a(n-36) +1441792*a(n-37) +2883584*a(n-38) -11534336*a(n-39) -5767168*a(n-40) +23068672*a(n-41) +262144*a(n-42) -1048576*a(n-43) -2097152*a(n-44) +8388608*a(n-45) +4194304*a(n-46) -16777216*a(n-47)

A221664 Sum of neighbor maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 n X 3 array.

Original entry on oeis.org

8, 64, 512, 3772, 32768, 262144, 2097152, 16777216, 134140928, 1073741824, 8589934592, 68719476736, 549755813888, 4398033385216, 35184372088832, 281474976710656, 2251799813685248, 18014398509481984, 144115185909972992
Offset: 1

Views

Author

R. H. Hardin, Jan 21 2013

Keywords

Comments

Column 3 of A221666.

Examples

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

Crossrefs

Cf. A221666.

Formula

Empirical: a(n) = 8*a(n-1) +360*a(n-5) -2880*a(n-6) -47232*a(n-10) +377856*a(n-11) +2872320*a(n-15) -22978560*a(n-16) -92491776*a(n-20) +739934208*a(n-21) +1689550848*a(n-25) -13516406784*a(n-26) -18150850560*a(n-30) +145206804480*a(n-31) +113850187776*a(n-35) -910801502208*a(n-36) -386547056640*a(n-40) +3092376453120*a(n-41) +549755813888*a(n-45) -4398046511104*a(n-46).

A221667 Sum of neighbor maps: number of 2 X n binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 2 X n array.

Original entry on oeis.org

4, 12, 64, 256, 992, 4096, 16384, 65344, 262144, 1048576, 4193280, 16777216, 67108864, 268430336, 1073741824, 4294967296, 17179844608, 68719476736, 274877906944, 1099511513088, 4398046511104, 17592186044416, 70368743653376
Offset: 1

Views

Author

R. H. Hardin, Jan 21 2013

Keywords

Comments

Row 2 of A221666.

Examples

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

Crossrefs

Cf. A221666.

Formula

Empirical: a(n) = 4*a(n-1) + 8*a(n-3) - 32*a(n-4) - 16*a(n-6) + 64*a(n-7).
Empirical g.f.: 4*x*(1 - x + 4*x^2 - 8*x^3 + 16*x^6) / ((1 - 4*x)*(1 - 4*x^3)^2). - Colin Barker, Aug 10 2018

A221668 Sum of neighbor maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 3Xn array.

Original entry on oeis.org

8, 48, 512, 3772, 31744, 262144, 2097152, 16728064, 134140928, 1073741824, 8587837440, 68719476736, 549755813888, 4397939335680, 35184372088832, 281474976710656, 2251796592459776, 18014398509481984, 144115185909972992
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Row 3 of A221666

Examples

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

A221665 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 nX4 array.

Original entry on oeis.org

16, 256, 3772, 63200, 1048576, 16777216, 268281856, 4294967296, 68702508544, 1099511627776, 17592133540864, 281474976710656, 4503599627370496
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Column 4 of A221666

Examples

			Some solutions for n=3
..0..1..0..0....0..1..1..0....0..1..0..0....1..1..0..0....0..0..0..1
..1..0..1..1....1..1..0..1....1..1..0..0....0..0..0..1....0..0..0..1
..0..1..0..1....1..1..0..1....0..1..1..0....1..1..1..1....1..1..0..0
		
Showing 1-5 of 5 results.