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.

A185771 Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock sum equal to any horizontal or vertical neighbor 2 X 2 subblock sum.

Original entry on oeis.org

81, 558, 3844, 26784, 186624, 1296000, 9000000, 62568000, 434972736, 3022785216, 21006444096, 146001569472, 1014758051904, 7052535822528, 49014897132096, 340658500222656, 2367611084874816, 16455017381102784, 114363207176279616
Offset: 1

Views

Author

R. H. Hardin Feb 03 2011

Keywords

Comments

Column 1 of A185777.

Examples

			Some solutions for 3 X 2:
..2..1....0..2....2..1....2..1....0..1....0..2....1..2....0..0....2..1....0..1
..0..2....2..2....0..1....1..1....2..1....1..0....2..0....2..1....0..2....0..2
..0..0....0..0....1..0....0..2....2..0....2..2....1..1....1..1....1..1....2..2
		

Formula

Empirical: a(n)= 3*a(n-1) +96*a(n-3) +504*a(n-4) +792*a(n-5) +2304*a(n-6) -13824*a(n-8) -13824*a(n-9).
Empirical: G.f.: -x*(-81 -315*x -2170*x^2 -7476*x^3 -11880*x^4 -21720*x^5 +25200*x^6 +177120*x^7 +155520*x^8) / ( (24*x^3+24*x^2+3*x-1) *(576*x^6-72*x^4-24*x^2-1) ). - R. J. Mathar, Jan 08 2015

A185772 Number of (n+1)X3 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.

Original entry on oeis.org

558, 7074, 89118, 1151346, 14837270, 190416934, 2442333998, 31384892214, 403218559222, 5178525140438, 66503687019294, 854217043141534, 10971879636716262, 140921116729079306, 1809957986000195766
Offset: 1

Views

Author

R. H. Hardin Feb 03 2011

Keywords

Comments

Column 2 of A185777

Examples

			Some solutions for 5X3
..0..0..1....0..0..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..1..0....0..2..1....0..2..1....2..0..0....0..0..1....0..1..1....2..1..0
..2..2..1....0..2..2....0..1..1....2..0..1....1..1..1....1..2..2....0..2..1
..2..2..2....0..1..1....0..1..0....0..1..0....1..2..0....0..0..1....2..0..0
..1..0..2....1..0..1....0..2..2....0..0..2....1..0..1....0..0..0....1..0..1
		

Formula

Empirical: a(n)=4*a(n-1)+49*a(n-2)+314*a(n-3)+6877*a(n-4)+3940*a(n-5)-66775*a(n-6)-5562*a(n-7)-4516042*a(n-8)-952177*a(n-9)+71657458*a(n-10)-81683756*a(n-11)+184951931*a(n-12)+934817466*a(n-13)-7278405891*a(n-14)+7577729242*a(n-15)+5409797117*a(n-16)-86907135378*a(n-17)+309915243239*a(n-18)-296185695772*a(n-19)-351845219222*a(n-20)+2892493385309*a(n-21)-6776522538782*a(n-22)+7058806126978*a(n-23)+3072790754210*a(n-24)-36661888510776*a(n-25)+74529700974096*a(n-26)-99999386996272*a(n-27)+60088842944712*a(n-28)+103959616747112*a(n-29)-313028645104464*a(n-30)+647329684563024*a(n-31)-801957721699232*a(n-32)+462840922316896*a(n-33)+384543021771136*a(n-34)-1781626290831168*a(n-35)+2738855357159040*a(n-36)-2209303681856256*a(n-37)-37689070540032*a(n-38)+2062920284706816*a(n-39)-2596060047154176*a(n-40)+2000380200560640*a(n-41)+81405399085056*a(n-42)-821157072150528*a(n-43)-122931731054592*a(n-44)+539315323600896*a(n-45)-332725569454080*a(n-46)+150115209707520*a(n-47)-33022594252800*a(n-48)

A185773 Number of (n+1)X4 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.

Original entry on oeis.org

3844, 89118, 2046098, 48744342, 1154712762, 27239862108, 641595944400, 15156754839024, 357869357090800, 8446854770875602, 199334639825139922, 4705555692884330894, 111074885127703334276, 2621814014876365014966
Offset: 1

Views

Author

R. H. Hardin Feb 03 2011

Keywords

Comments

Column 3 of A185777

Examples

			Some solutions for 3X4
..2..1..0..2....2..1..1..1....2..2..0..1....1..1..2..2....0..0..0..1
..1..1..0..2....2..0..0..1....2..0..0..2....0..1..1..1....0..1..2..1
..0..0..2..1....1..1..2..2....0..2..1..2....0..1..1..2....1..2..2..0
		

A185774 Number of (n+1)X5 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.

Original entry on oeis.org

26784, 1151346, 48744342, 2171002788, 95851024672, 4212755548948, 184696487434352, 8130440303768416, 357605861336206826, 15723990359863559644, 691174683753522142476, 30395002285452611004698
Offset: 1

Views

Author

R. H. Hardin Feb 03 2011

Keywords

Comments

Column 4 of A185777

Examples

			Some solutions for 3X5
..0..1..0..1..0....0..0..0..0..1....0..1..2..2..2....0..2..2..1..1
..0..1..2..2..0....0..2..2..0..2....0..0..2..1..1....0..0..1..0..1
..1..2..1..2..0....0..1..1..2..0....1..1..1..2..1....1..0..2..2..1
		

A185770 Number of (n+1)X(n+1) 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.

Original entry on oeis.org

81, 7074, 2046098, 2171002788, 7861640359954
Offset: 1

Views

Author

R. H. Hardin Feb 03 2011

Keywords

Comments

Diagonal of A185777

Examples

			Some solutions for 3X3
..2..1..2....0..0..1....2..0..0....2..1..1....1..2..1....1..1..0....2..1..1
..0..2..2....1..1..2....1..1..0....2..0..1....0..1..2....1..0..0....0..0..0
..0..1..0....0..1..1....2..2..1....1..1..0....2..0..1....2..1..1....0..2..2
		

A185775 Number of (n+1)X6 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.

Original entry on oeis.org

186624, 14837270, 1154712762, 95851024672, 7861640359954, 641850855452998
Offset: 1

Views

Author

R. H. Hardin Feb 03 2011

Keywords

Comments

Column 5 of A185777

Examples

			Some solutions for 3X6
..0..0..1..2..0..0....0..0..1..2..1..2....0..0..2..2..0..0....0..0..1..2..2..2
..0..1..2..0..0..1....0..1..2..2..1..0....0..0..1..0..2..1....0..0..0..1..2..2
..0..1..2..0..0..1....0..1..1..1..0..2....0..1..0..0..0..2....0..1..1..1..0..1
		

A185776 Number of (n+1)X7 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.

Original entry on oeis.org

1296000, 190416934, 27239862108, 4212755548948, 641850855452998
Offset: 1

Views

Author

R. H. Hardin Feb 03 2011

Keywords

Comments

Column 6 of A185777

Examples

			Some solutions for 3X7
..0..0..1..2..0..2..2....0..0..1..1..2..1..0....0..0..1..0..2..1..2
..0..1..0..0..0..2..2....0..2..0..2..2..0..0....0..0..0..2..1..2..0
..0..1..1..1..0..0..2....0..1..1..2..2..0..2....0..1..1..1..2..2..2
		
Showing 1-7 of 7 results.