A230675 -id:A230675 - cp's OEIS frontend

A230670 Number of n X 3 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

3, 87, 1173, 17271, 251595, 3669765, 53519163, 780527655, 11383251453, 166013909415, 2421155095347, 35310246222069, 514966385300499, 7510295349852327, 109530520538219973, 1597398553655896551

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Column 3 of A230675.

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

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

Empirical: a(n) = 14*a(n-1) +9*a(n-2) -9*a(n-3) +30*a(n-4) -19*a(n-5).

Empirical g.f.: 3*x*(1 + 15*x - 24*x^2 + 31*x^3 - 21*x^4) / (1 - 14*x - 9*x^2 + 9*x^3 - 30*x^4 + 19*x^5). - Colin Barker, Feb 09 2018

A230671 Number of nX4 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

9, 513, 18915, 730503, 28368687, 1100265795, 42681522741, 1655698076319, 64227455495727, 2491499259313149, 96649752790452639, 3749218360204902945, 145438947787185663525, 5641839307719342400131, 218857130513207098732227

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Column 4 of A230675

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

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

Empirical: a(n) = 37*a(n-1) +85*a(n-2) -427*a(n-3) -7212*a(n-4) +18333*a(n-5) -11460*a(n-6) -144161*a(n-7) +427156*a(n-8) -283771*a(n-9) -737876*a(n-10) +2778226*a(n-11) -6632316*a(n-12) +11370217*a(n-13) -12647443*a(n-14) +15533606*a(n-15) -15672799*a(n-16) +13230743*a(n-17) -12231559*a(n-18) +8238905*a(n-19) -5597330*a(n-20) +3725581*a(n-21) -1775475*a(n-22) +1133310*a(n-23) -535263*a(n-24) +157955*a(n-25) -84089*a(n-26) +33686*a(n-27) -7250*a(n-28) +372*a(n-29) +636*a(n-30) -360*a(n-31) +72*a(n-32)

A230672 Number of n X 5 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

15, 3387, 340563, 37034355, 4022141121, 436827078531, 47444197636239, 5152946201086569, 559664961809994753, 60785594007085980027, 6601964808003397959249, 717043900743978231419349

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Column 5 of A230675.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 80

Cf. A230675.

Empirical recurrence of order 80 (see link above).

A230673 Number of nX6 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

33, 21933, 6081561, 1844154933, 559929294657, 169908632412447, 51564141085334199, 15648664251672721725, 4749050405190938157075, 1441240135293669121537797, 437387035655507564724178683

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Column 6 of A230675

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

R. H. Hardin, Table of n, a(n) for n = 1..191

A230674 Number of nX7 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

63, 141411, 108108231, 91258562955, 77282148036051, 65376252475286079, 55314799986833459367, 46801278897512391365487, 39598077165834016051238043, 33503529630527901643288424553, 28346994197765512368139659784815

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Column 7 of A230675

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

R. H. Hardin, Table of n, a(n) for n = 1..39

A230676 Number of 2 X n 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 15, 87, 513, 3387, 21933, 141411, 913245, 5898099, 38088477, 245968275, 1588424445, 10257784563, 66243081501, 427786930899, 2762577674301, 17840272397235, 115209545904477, 744004305214611, 4804657476983421

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

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

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

Row 2 of A230675.

Empirical: a(n) = 5*a(n-1) + 6*a(n-2) + 20*a(n-3) + 12*a(n-4) + 8*a(n-5).

Empirical g.f.: 3*x^2*(5 + 4*x - 4*x^2) / (1 - 5*x - 6*x^2 - 20*x^3 - 12*x^4 - 8*x^5). - Colin Barker, Sep 22 2018

A230677 Number of 3Xn 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 81, 1173, 18915, 340563, 6081561, 108108231, 1923264723, 34219066161, 608809697883, 10831633601715, 192711252863829, 3428626492612815, 61000479835023903, 1085291316379044081, 19308983258977687575

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Row 3 of A230675

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

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

Empirical: a(n) = 13*a(n-1) +65*a(n-2) +312*a(n-3) +829*a(n-4) +559*a(n-5) -458*a(n-6) -2767*a(n-7) -2801*a(n-8) -1031*a(n-9) -485*a(n-10) -743*a(n-11) -272*a(n-12) +332*a(n-13) +172*a(n-14) -24*a(n-15) for n>16

A230678 Number of 4Xn 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 423, 17271, 730503, 37034355, 1844154933, 91258562955, 4522036938501, 224105728666527, 11105653159056021, 550345235166102387, 27272655718068842535, 1351510936295338591335, 66974836192708860686913

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Row 4 of A230675

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 64

Empirical recurrence of order 64 (see link above)

A230679 Number of 5 X n 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 2247, 251595, 28368687, 4022141121, 559929294657, 77282148036051, 10681855554910983, 1476794401334027865, 204155617303878631797, 28222820785777362856803, 3901584177313433415004191

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Row 5 of A230675.

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

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

Cf. A230675.

A230680 Number of 6Xn 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 11925, 3669765, 1100265795, 436827078531, 169908632412447, 65376252475286079, 25197971211829585887, 9715194049282171327617, 3745393333629058405378449, 1443910366341874206277548363

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Row 6 of A230675

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

R. H. Hardin, Table of n, a(n) for n = 1..33

cp's OEIS Frontend

A230670 Number of n X 3 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

Formula

A230671 Number of nX4 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

Formula

A230672 Number of n X 5 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A230673 Number of nX6 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

A230674 Number of nX7 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

A230676 Number of 2 X n 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A230677 Number of 3Xn 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

Formula

A230678 Number of 4Xn 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

Formula

A230679 Number of 5 X n 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A230680 Number of 6Xn 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Views

Author

Keywords

Comments

Examples

Links