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.

A209040 Number of n X n 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

Original entry on oeis.org

4, 124, 47700, 225262148, 13034933066892, 9239962457023110368, 80235179157233210417254036, 8534774056580607728132307076396612, 11121202754126311568095965858257048619933492
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Diagonal of A209047

Examples

			Some solutions for n=4
..3..1..2..3....3..2..3..1....2..3..1..0....1..0..2..1....3..1..2..1
..0..1..0..0....1..2..2..0....3..2..2..0....0..1..0..2....0..3..3..1
..1..0..3..0....2..3..1..3....2..3..3..0....2..1..0..3....3..1..3..3
..2..2..2..0....1..0..3..0....1..3..0..2....1..0..1..0....0..1..1..1
		

A209041 Number of n X 2 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

Original entry on oeis.org

12, 124, 1300, 13644, 143212, 1503212, 15778340, 165616044, 1738375148, 18246711388, 191525101396, 2010327432972, 21101236121548, 221487384867980, 2324824070641124, 24402324144347820, 256136983080016460
Offset: 1

Views

Author

R. H. Hardin, Mar 04 2012

Keywords

Comments

Column 2 of A209047.

Examples

			Some solutions for n=4:
..3..1....1..0....2..3....1..0....1..2....0..1....0..1....2..3....1..3....2..0
..1..2....0..1....1..0....2..3....2..3....3..0....1..3....1..0....0..1....1..0
..3..3....1..3....3..2....1..3....3..0....1..1....3..0....0..3....1..0....2..0
..0..1....2..2....2..0....3..1....2..0....2..0....0..1....1..0....2..0....1..2
		

Crossrefs

Cf. A209047.

Formula

Empirical: a(n) = 11*a(n-1) - 5*a(n-2) - 3*a(n-3).
Empirical g.f.: 4*x*(1 - x)*(3 + x) / (1 - 11*x + 5*x^2 + 3*x^3). - Colin Barker, Jul 08 2018

A209042 Number of n X 3 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

Original entry on oeis.org

36, 1300, 47700, 1752148, 64369764, 2364812680, 86878417604, 3191736905988, 117257942776700, 4307819083344444, 158260539240359944, 5814171346741659592, 213600867349885236600, 7847262801829583566600, 288292525423375500733688
Offset: 1

Views

Author

R. H. Hardin, Mar 04 2012

Keywords

Comments

Column 3 of A209047.

Examples

			Some solutions for n=4
..0..1..0....0..1..2....2..1..2....2..0..1....1..0..2....1..3..0....1..0..1
..3..3..2....3..3..0....3..0..2....0..2..0....3..2..1....2..1..3....0..1..3
..1..3..1....0..1..1....2..0..0....1..2..2....1..0..3....0..1..0....1..2..1
..2..3..3....3..3..1....1..3..0....3..0..0....3..0..1....1..2..0....0..2..3
		

Crossrefs

Cf. A209047.

Formula

Empirical: a(n) = 23*a(n-1) +491*a(n-2) +570*a(n-3) -2219*a(n-4) -7882*a(n-5) -12517*a(n-6) -6376*a(n-7) -1205*a(n-8) -6747*a(n-9) +4080*a(n-10) +7811*a(n-11) -4675*a(n-12) +1790*a(n-13) +2576*a(n-14) -2905*a(n-15) +513*a(n-16) +621*a(n-17) -27*a(n-18) -81*a(n-19).
Formula confirmed by Robert Israel, Apr 03 2018 (see link).

A209043 Number of nX4 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

Original entry on oeis.org

108, 13644, 1752148, 225262148, 28964458546, 3724317998214, 478881915072688, 61575811582924326, 7917568966250856112, 1018060448767393518568, 130904710995247416149996, 16832049002507023710858048
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 4 of A209047

Examples

			Some solutions for n=4
..1..3..2..1....3..1..2..3....2..3..1..3....2..0..1..0....0..1..0..3
..2..2..1..2....0..1..0..0....3..2..1..1....3..0..1..2....2..2..2..2
..0..2..0..3....1..0..3..0....0..2..0..1....1..3..0..0....1..1..3..2
..1..0..2..1....2..2..2..0....1..3..3..1....2..3..2..2....0..3..0..0
		

Formula

Empirical: a(n) = 81*a(n-1) +6019*a(n-2) +17676*a(n-3) -599593*a(n-4) -4088888*a(n-5) -3730999*a(n-6) +101900822*a(n-7) +392580866*a(n-8) -1523969122*a(n-9) -1305957528*a(n-10) +28806814857*a(n-11) -138610167727*a(n-12) -92479090429*a(n-13) +1908411722538*a(n-14) -4688061743329*a(n-15) +868176994167*a(n-16) +37238901400055*a(n-17) -108429686426996*a(n-18) +63224602311532*a(n-19) +146638886828725*a(n-20) -399120237191674*a(n-21) +643043970497948*a(n-22) +657212030688884*a(n-23) -3350737459002767*a(n-24) -512333788345638*a(n-25) +9658795596391494*a(n-26) -7307540288812320*a(n-27) +4046894684677414*a(n-28) -49280938427249*a(n-29) -15919719904208233*a(n-30) +5309011068556252*a(n-31) -27520223522274361*a(n-32) -15861006441701489*a(n-33) +40304491599363659*a(n-34) +82471636953173637*a(n-35) +47893641143347577*a(n-36) -40160830349734528*a(n-37) -42797055661074986*a(n-38) -77937400975405899*a(n-39) -41530998228072484*a(n-40) +13888895933404573*a(n-41) +29183625221012494*a(n-42) +57292324471563068*a(n-43) +24864119964192191*a(n-44) -8835195495823362*a(n-45) -12319214526059338*a(n-46) -1662673048234914*a(n-47) +3583743936817358*a(n-48) -188032462140047*a(n-49) -184935511247693*a(n-50) +57632509822517*a(n-51) +92193118733688*a(n-52) -31500301490757*a(n-53) +6805810881792*a(n-54) +8054118978759*a(n-55) +514316253699*a(n-56) -51314595768*a(n-57) +41840052498*a(n-58) +7462586376*a(n-59) +4099260312*a(n-60) -90167823*a(n-61) -35429400*a(n-62) +1062882*a(n-63)

A209044 Number of nX5 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

Original entry on oeis.org

324, 143212, 64369764, 28964458546, 13034933066892, 5866193355938718, 2640002203816927226, 1188097914449381928076, 534687682738799964386512, 240629088538426121775581624, 108291924647368035417996430328
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 5 of A209047

Examples

			Some solutions for n=4
..0..1..3..0..1....1..0..3..0..3....1..3..2..3..0....2..0..3..0..2
..1..2..0..2..2....2..2..3..2..2....2..2..1..1..0....0..3..1..1..2
..2..0..3..2..3....3..2..3..2..3....1..1..2..2..2....1..3..0..1..0
..0..2..3..3..0....0..2..1..2..1....0..0..3..0..0....3..2..2..1..2
		

A209045 Number of nX6 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

Original entry on oeis.org

972, 1503212, 2364812680, 3724317998214, 5866193355938718, 9239962457023110368, 14554067523333615991960, 22924432479225632829691864, 36108778942762030367945973348, 56875733727363424301468394080962
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 6 of A209047

Examples

			Some solutions for n=4
..0..1..0..3..2..3....2..0..1..2..0..2....2..3..1..0..1..3....0..3..0..1..0..3
..1..2..2..1..3..2....3..0..1..3..2..0....0..0..1..1..2..3....3..0..2..1..0..1
..0..3..3..0..1..3....0..1..0..1..0..1....3..3..3..0..0..2....0..1..1..0..3..3
..2..1..1..2..1..1....3..3..3..3..3..0....1..1..3..1..0..0....1..2..3..3..0..3
		

A209046 Number of nX7 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

Original entry on oeis.org

2916, 15778340, 86878417604, 478881915072688, 2640002203816927226, 14554067523333615991960, 80235179157233210417254036, 442328880747673272994524595152, 2438516891360121789946284774426192
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 7 of A209047

Examples

			Some solutions for n=4
..0..3..0..1..0..3..0....2..0..3..0..3..2..3....3..2..0..1..0..3..0
..3..2..2..0..1..0..1....0..1..3..0..3..2..1....1..3..2..2..2..1..2
..1..0..3..2..1..2..3....1..2..2..3..0..0..1....2..0..2..3..1..3..1
..3..0..3..2..2..0..1....0..3..3..0..3..1..3....0..3..3..0..2..1..3
		
Showing 1-7 of 7 results.