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 12 results. Next

A218892 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 n X 3 array.

Original entry on oeis.org

4, 18, 72, 286, 1162, 4700, 19046, 77198, 312944, 1268694, 5143506, 20852924, 84542894, 342758566, 1389632608, 5633935678, 22841460250, 92605309212, 375446383830, 1522158836638, 6171234143440, 25019814013190, 101436937848962
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2012

Keywords

Comments

Column 3 of A218897.

Examples

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

Crossrefs

Cf. A218897.

Formula

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 5*a(n-3) - 8*a(n-4) - 4*a(n-5).
Empirical g.f.: 2*x*(2 + x - 4*x^2 - 9*x^3 - 2*x^4) / (1 - 4*x - 2*x^2 + 5*x^3 + 8*x^4 + 4*x^5). - Colin Barker, Jul 24 2018

A218893 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 n X 4 array.

Original entry on oeis.org

6, 34, 212, 1096, 6422, 35812, 202662, 1143320, 6451714, 36412818, 205486910, 1159668470, 6544517458, 36933689524, 208433556616, 1176284907448, 6638308849796, 37462983914486, 211420591173616, 1193142178688764
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2012

Keywords

Comments

Column 4 of A218897.

Examples

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

Crossrefs

Cf. A218897.

Formula

Empirical: a(n) = 6*a(n-1) +3*a(n-2) -25*a(n-3) -29*a(n-4) +53*a(n-5) +33*a(n-6) +12*a(n-7) -38*a(n-8) -18*a(n-10) +12*a(n-11) -15*a(n-12) +7*a(n-13) +4*a(n-14).

A218894 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 nX5 array.

Original entry on oeis.org

10, 86, 786, 6280, 54726, 463746, 3960146, 33785542, 288335090, 2461034914, 21006978672, 179319456042, 1530738564878, 13067135278520, 111548343657960, 952243061730174, 8128934949226332, 69393715746097124, 592389051962076448
Offset: 1

Views

Author

R. H. Hardin Nov 08 2012

Keywords

Comments

Column 5 of A218897

Examples

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

Formula

Empirical: a(n) = 12*a(n-1) -13*a(n-2) -154*a(n-3) -64*a(n-4) +1337*a(n-5) +1762*a(n-6) -4536*a(n-7) -11750*a(n-8) +3034*a(n-9) +33505*a(n-10) +16287*a(n-11) -53890*a(n-12) -50327*a(n-13) +94513*a(n-14) +109573*a(n-15) -153231*a(n-16) -236409*a(n-17) +131361*a(n-18) +324124*a(n-19) -42391*a(n-20) -192220*a(n-21) +114526*a(n-22) +130510*a(n-23) -108443*a(n-24) -223161*a(n-25) -66803*a(n-26) +28885*a(n-27) +14553*a(n-28) +44272*a(n-29) +50715*a(n-30) +26319*a(n-31) +1067*a(n-32) +4726*a(n-33) -18580*a(n-34) -3660*a(n-35) -1512*a(n-36) +64*a(n-37)

A218895 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 nX6 array.

Original entry on oeis.org

16, 180, 2594, 28598, 373612, 4575512, 57116962, 710022390, 8831593874, 109858747456, 1366468080924, 16997248406138, 211423793938568, 2629844586659292, 32711934936773636, 406895021195875512
Offset: 1

Views

Author

R. H. Hardin Nov 08 2012

Keywords

Comments

Column 6 of A218897

Examples

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

A218896 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 nX7 array.

Original entry on oeis.org

26, 426, 9110, 149238, 2880294, 52413310, 969423130, 17870306268, 329607859688, 6079480914622, 112133703714680, 2068302082008760, 38149959135417738, 703681415905779954, 12979537903131358604, 239410417049738535252
Offset: 1

Views

Author

R. H. Hardin Nov 08 2012

Keywords

Comments

Column 7 of A218897

Examples

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

A218898 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 2 X n array.

Original entry on oeis.org

4, 6, 18, 34, 86, 180, 426, 930, 2140, 4758, 10818, 24240, 54834, 123274, 278260, 626446, 1412746, 3182416, 7174106, 16164834, 36434260, 82103270, 185041218, 417002816, 939796802, 2117936730, 4773120596, 10756848350, 24242204506
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2012

Keywords

Comments

Row 2 of A218897.

Examples

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

Crossrefs

Cf. A218897.

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) - 2*a(n-5).
Empirical g.f.: 2*x*(2 + x - x^3 - x^4) / (1 - x - 3*x^2 + 2*x^5). - Colin Barker, Jul 24 2018

A218899 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 3Xn array.

Original entry on oeis.org

8, 16, 72, 212, 786, 2594, 9110, 31062, 107510, 369596, 1274760, 4390640, 15132044, 52139518, 179669784, 619118588, 2133406676, 7351495186, 25332356634, 87292564824, 300799972600, 1036523262982, 3571740490936, 12307815695422
Offset: 1

Views

Author

R. H. Hardin Nov 08 2012

Keywords

Comments

Row 3 of A218897

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +7*a(n-2) -4*a(n-3) -6*a(n-4) -10*a(n-5) -20*a(n-6) +15*a(n-7) -a(n-8) +22*a(n-9) +14*a(n-10) -5*a(n-11) -6*a(n-13) -2*a(n-14)

A218900 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 4Xn array.

Original entry on oeis.org

16, 38, 286, 1096, 6280, 28598, 149238, 722094, 3651696, 18021788, 90208322, 448024152, 2235168520, 11123412124, 55435126828, 276050589212, 1375270796150, 6849815881386, 34121765700892, 169961133958828, 846617625629670
Offset: 1

Views

Author

R. H. Hardin Nov 08 2012

Keywords

Comments

Row 4 of A218897

Examples

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

Formula

Empirical: a(n) = 3*a(n-1) +16*a(n-2) -16*a(n-3) -51*a(n-4) -107*a(n-5) -115*a(n-6) +457*a(n-7) +511*a(n-8) +617*a(n-9) -294*a(n-10) -2046*a(n-11) -1191*a(n-12) -307*a(n-13) +1059*a(n-14) +3506*a(n-15) -419*a(n-16) -2054*a(n-17) -800*a(n-18) -301*a(n-19) +699*a(n-20) +1069*a(n-21) +108*a(n-22) -403*a(n-23) -292*a(n-24) -177*a(n-25) +156*a(n-26) +98*a(n-27) +52*a(n-28) -72*a(n-29) +8*a(n-30)

A218901 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 5Xn array.

Original entry on oeis.org

32, 98, 1162, 6422, 54726, 373612, 2880294, 20982806, 157437728, 1166572286, 8697719814, 64700267892, 481788660634, 3586697140250, 26703604337056, 198819608617794, 1480252390312110, 11021165108877556, 82055993062915878
Offset: 1

Views

Author

R. H. Hardin Nov 08 2012

Keywords

Comments

Row 5 of A218897

Examples

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

A218902 Number of 6Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 6Xn array.

Original entry on oeis.org

64, 244, 4700, 35812, 463746, 4575512, 52413310, 560696174, 6215491022, 67904677040, 747179229166, 8201691157406, 90124453206806, 990167833005856, 10878984112533098, 119537916859104756, 1313402969442315846
Offset: 1

Views

Author

R. H. Hardin Nov 08 2012

Keywords

Comments

Row 6 of A218897

Examples

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