A251373 -id:A251373 - cp's OEIS frontend

A251366 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.

79, 695, 6113, 53769, 472943, 4159927, 36590017, 321839625, 2830847119, 24899654327, 219013164449, 1926402895881, 16944315318191, 149039342816695, 1310924949760897, 11530674997804041, 101421874630758607

Offset: 1

R. H. Hardin, Dec 01 2014

Column 1 of A251373.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Maple-assisted proof of formula
Index entries for linear recurrences with constant coefficients, signature (8,7).

Cf. A251373, A254598.

f:= gfun:-rectoproc({a(n) = 8*a(n-1) + 7*a(n-2), a(1)=
79, a(2)=695},a(n),remember):
map(f, [$1..40]); # Robert Israel, Mar 19 2018

LinearRecurrence[{8, 7}, {79, 695}, 40] (* Jean-François Alcover, Aug 19 2022 *)

Empirical: a(n) = 8*a(n-1) + 7*a(n-2).
Empirical g.f.: x*(79 + 63*x) / (1 - 8*x - 7*x^2). - Colin Barker, Mar 19 2018
Empirical formula verified: see link.
a(n) = A254598(n+1). - Robert Israel, Mar 19 2018

A251365 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

Original entry on oeis.org

79, 17969, 35257505, 597108952883, 87274898497023663, 110094177769643072247073, 1198610045118318903896947691841, 112623783277770500761933316031229772803

Offset: 1

R. H. Hardin, Dec 01 2014

nonn

Diagonal of A251373

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

R. H. Hardin, Table of n, a(n) for n = 1..12

A251367 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock summing to 1, 2, 3, 4, 5, 6, or 7.

Original entry on oeis.org

695, 17969, 464393, 12002283, 310199103, 8017100977, 207202101873, 5355141623323, 138403720518311, 3577046360518609, 92448820142650873, 2389341228591410219, 61752562096926105327, 1595995950642355498897

Offset: 1

R. H. Hardin, Dec 01 2014

nonn

Column 2 of A251373.

			Some solutions for n=2:
  2 1 1   2 0 2   0 2 1   2 2 2   0 0 2   0 0 2   0 0 2
  0 0 0   1 0 0   1 0 1   0 1 1   1 1 2   1 2 1   1 1 1
  1 2 2   2 0 1   1 2 1   2 0 2   0 0 1   1 0 1   0 1 0

R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Maple-assisted proof of empirical formula
Index entries for linear recurrences with constant coefficients, signature (24,49,-34).

f:= gfun:-rectoproc({a(n) = 24*a(n-1) +49*a(n-2) -34*a(n-3),a(1)=695,a(2)=17969, a(3)=464393},a(n),remember):
map(f, [$1..30]); # Robert Israel, Mar 19 2018

Empirical: a(n) = 24*a(n-1) + 49*a(n-2) - 34*a(n-3).
From Robert Israel, Mar 19 2018: (Start)
Empirical formula verified: see link.
G.f.: (695*x+1289*x^2-918*x^3)/(1-24*x-49*x^2+34*x^3). (End)

A251368 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.

Original entry on oeis.org

6113, 464393, 35257505, 2676962017, 203249994369, 15431888950873, 1171676222709377, 88960280954218353, 6754367316602393761, 512829741092571856681, 38936932361040303524065, 2956311969073264569680513

Offset: 1

R. H. Hardin, Dec 01 2014

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 3 of A251373.

Empirical: a(n) = 66*a(n-1) + 746*a(n-2) + 660*a(n-3) - 6281*a(n-4) + 3690*a(n-5).

Empirical g.f.: x*(6113 + 60935*x + 47269*x^2 - 505071*x^3 + 298890*x^4) / (1 - 66*x - 746*x^2 - 660*x^3 + 6281*x^4 - 3690*x^5). - Colin Barker, Nov 29 2018

A251369 Number of (n+1)X(4+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

Original entry on oeis.org

53769, 12002283, 2676962017, 597108952883, 133187012365193, 29707797738391051, 6626420822196876929, 1478044705717848217587, 329682676296148787924297, 73536792652326563411377515

Offset: 1

R. H. Hardin, Dec 01 2014

nonn

Column 4 of A251373

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 200*a(n-1) +5284*a(n-2) -29042*a(n-3) -605899*a(n-4) +5424778*a(n-5) -14965624*a(n-6) +12176608*a(n-7) +6786256*a(n-8) -7898208*a(n-9) -2471040*a(n-10)

A251370 Number of (n+1)X(5+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

Original entry on oeis.org

472943, 310199103, 203249994369, 133187012365193, 87274898497023663, 57189617044768555919, 37475289004151496747521, 24556857847572938143153273, 16091650870807332663609588335, 10544558647186113778424744945247

Offset: 1

R. H. Hardin, Dec 01 2014

nonn

Column 5 of A251373

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 554*a(n-1) +65999*a(n-2) +392514*a(n-3) -99331406*a(n-4) +224864516*a(n-5) +58176387190*a(n-6) -1094924130348*a(n-7) +7544081453779*a(n-8) -11449965654350*a(n-9) -96842972469581*a(n-10) +329620771232346*a(n-11) +513725000610028*a(n-12) -2276947870826176*a(n-13) -2431866003930568*a(n-14) +5792326731737520*a(n-15) +8728840892325056*a(n-16) +1282895896780288*a(n-17) -2096430751248384*a(n-18) -337501235220480*a(n-19) +173155321036800*a(n-20)

A251371 Number of (n+1)X(6+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

Original entry on oeis.org

4159927, 8017100977, 15431888950873, 29707797738391051, 57189617044768555919, 110094177769643072247073, 211939290252887391404913105, 407998534122358956249893397419

Offset: 1

R. H. Hardin, Dec 01 2014

nonn

Column 6 of A251373

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

R. H. Hardin, Table of n, a(n) for n = 1..210

A251372 Number of (n+1) X (7+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.

Original entry on oeis.org

36590017, 207202101873, 1171676222709377, 6626420822196876929, 37475289004151496747521, 211939290252887391404913105, 1198610045118318903896947691841, 6778667859264959218007000710080097

Offset: 1

R. H. Hardin, Dec 01 2014

nonn

Column 7 of A251373.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A251373.

cp's OEIS Frontend

A251366 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.

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A251365 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

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A251367 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock summing to 1, 2, 3, 4, 5, 6, or 7.

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A251368 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.

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A251369 Number of (n+1)X(4+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

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A251370 Number of (n+1)X(5+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

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A251371 Number of (n+1)X(6+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

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A251372 Number of (n+1) X (7+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.

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