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 1-7 of 7 results.

A221066 Sum of neighbor maps: number of n X 2 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 n X 2 array.

Original entry on oeis.org

2, 8, 20, 56, 168, 476, 1364, 3952, 11360, 32692, 94236, 271352, 781432, 2250892, 6482724, 18670784, 53775312, 154880036, 446074860, 1284760776, 3700290152, 10657349244, 30694667380, 88404940816, 254618597952, 733337259924
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2012

Keywords

Comments

Column 2 of A221072.

Examples

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

Crossrefs

Cf. A221072.

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + 4*a(n-3) - 5*a(n-4) - 6*a(n-5).
Empirical g.f.: 2*x*(1 + x)*(1 + x - x^2 - 3*x^3) / (1 - 2*x - 2*x^2 - 4*x^3 + 5*x^4 + 6*x^5). - Colin Barker, Aug 03 2018

A221067 Sum of neighbor maps: number of nX3 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 nX3 array.

Original entry on oeis.org

8, 20, 512, 4096, 26976, 262144, 2097152, 16401664, 134217728, 1073741824, 8572235776, 68719476736, 549755813888, 4397319143424, 35184372088832, 281474976710656, 2251771635433472, 18014398509481984, 144115188075855872
Offset: 1

Views

Author

R. H. Hardin Dec 31 2012

Keywords

Comments

Column 3 of A221072

Examples

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

Formula

Empirical: a(n) = 8*a(n-1) +160*a(n-3) -1280*a(n-4) -11200*a(n-6) +89600*a(n-7) +453632*a(n-9) -3629056*a(n-10) -11841536*a(n-12) +94732288*a(n-13) +209715200*a(n-15) -1677721600*a(n-16) -2577661952*a(n-18) +20621295616*a(n-19) +22041067520*a(n-21) -176328540160*a(n-22) -128781910016*a(n-24) +1030255280128*a(n-25) +490700013568*a(n-27) -3925600108544*a(n-28) -1099511627776*a(n-30) +8796093022208*a(n-31) +1099511627776*a(n-33) -8796093022208*a(n-34)

A221068 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 nX4 array.

Original entry on oeis.org

16, 56, 4096, 65536, 829184, 16777216, 268435456, 4185880576, 68719476736, 1099511627776, 17551735783424, 281474976710656, 4503599627370496, 72044225131708416, 1152921504606846976, 18446744073709551616
Offset: 1

Views

Author

R. H. Hardin Dec 31 2012

Keywords

Comments

Column 4 of A221072

Examples

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

Formula

Empirical: a(n) = 16*a(n-1) +1280*a(n-3) -20480*a(n-4) -726016*a(n-6) +11616256*a(n-7) +243236864*a(n-9) -3891789824*a(n-10) -54177169408*a(n-12) +866834710528*a(n-13) +8559911763968*a(n-15) -136958588223488*a(n-16) -999099251818496*a(n-18) +15985588029095936*a(n-19) +88516761267208192*a(n-21) -1416268180275331072*a(n-22) -6065057600834109440*a(n-24) +97040921613345751040*a(n-25) +325521958426885750784*a(n-27) -5208351334830172012544*a(n-28) -13798310784589052772352*a(n-30) +220772972553424844357632*a(n-31) +463933643691908201971712*a(n-33) -7422938299070531231547392*a(n-34) -12381420039132312466620416*a(n-36) +198102720626116999465926656*a(n-37) +261460839310197953740668928*a(n-39) -4183373428963167259850702848*a(n-40) -4335676130609162821497257984*a(n-42) +69370818089746605143956127744*a(n-43) +55704888638569365981756391424*a(n-45) -891278218217109855708102262784*a(n-46) -542593184231850628678886096896*a(n-48) +8681490947709610058862177550336*a(n-49) +3868852764963520870061692682240*a(n-51) -61901644239416333920987082915840*a(n-52) -19030852223934150966024236695552*a(n-54) +304493635582946415456387787128832*a(n-55) +57678102310384437768099995844608*a(n-57) -922849636966151004289599933513728*a(n-58) -81129638414606681695789005144064*a(n-60) +1298074214633706907132624082305024*a(n-61)

A221065 Sum of neighbor maps: number of n X n binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 n X n array.

Original entry on oeis.org

2, 8, 512, 65536, 17530176, 68719476736, 562949953421312
Offset: 1

Views

Author

R. H. Hardin Dec 31 2012

Keywords

Comments

Diagonal of A221072

Examples

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

A221069 Sum of neighbor maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 nX5 array.

Original entry on oeis.org

24, 168, 26976, 829184, 17530176, 811440640, 25241048576
Offset: 1

Views

Author

R. H. Hardin Dec 31 2012

Keywords

Comments

Column 5 of A221072

Examples

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

A221070 Sum of neighbor maps: number of n X 6 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 n X 6 array.

Original entry on oeis.org

64, 476, 262144, 16777216, 811440640, 68719476736, 4398046511104, 275046044778496, 18014398509481984, 1152921504606846976, 73666094089946267648
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2012

Keywords

Comments

Column 6 of A221072.

Examples

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

Crossrefs

Cf. A221072.

A221071 Sum of neighbor maps: number of nX7 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 nX7 array.

Original entry on oeis.org

128, 1364, 2097152, 268435456, 25241048576, 4398046511104, 562949953421312, 70342550622109696
Offset: 1

Views

Author

R. H. Hardin Dec 31 2012

Keywords

Comments

Column 7 of A221072

Examples

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