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 10 results.

A239594 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 3, 4, 4, 5, 7, 8, 11, 12, 16, 19, 24, 30, 36, 46, 55, 70, 85, 106, 131, 161, 201, 246, 307, 377, 468, 578, 714, 885, 1091, 1353, 1669, 2067, 2554, 3158, 3907, 4827, 5974, 7381, 9132, 11288, 13959, 17262, 21340, 26394, 32628, 40353, 49890, 61693, 76284, 94321
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Examples

			All solutions for n=4:
..2..0....2..0....3..0....2..0
..2..0....2..0....2..3....2..0
..3..0....2..0....3..2....3..0
..2..3....2..0....2..3....3..2
		

Crossrefs

Column 2 of A239599.

Formula

Empirical: a(n) = a(n-2) + a(n-5) for n>6.
Empirical g.f.: x*(4 + 3*x + x^3 + x^4 - x^5) / (1 - x^2 - x^5). - Colin Barker, Oct 26 2018

A239595 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

10, 15, 31, 82, 177, 458, 1071, 2150, 5209, 11204, 24273, 58130, 123647, 278779, 634283, 1360984, 3103558, 6892041, 15084730, 34250268, 75240998, 167095718, 375589317, 825397281, 1846103269, 4114306092, 9085354958, 20337008173
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Column 3 of A239599

Examples

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

A239596 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

24, 64, 187, 643, 1737, 7461, 24946, 78667, 313003, 946740, 3353070, 11758390, 36733281, 134840254, 447239565, 1494320065, 5328884020, 17359223415, 60336682303, 207461258909, 687759739866, 2406912915998, 8088972710842
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Column 4 of A239599

Examples

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

A239597 Number of n X 5 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

56, 244, 1310, 8773, 38824, 282333, 1583770, 8002162, 56967196, 275601241, 1652784297, 9647550002, 46816042965, 300001108431, 1594217578916, 8755494803789, 53058504883026, 272797119276412, 1625241123981520
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Column 5 of A239599.

Examples

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

Crossrefs

Cf. A239599.

A239600 Number of 2Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

3, 3, 15, 64, 244, 1030, 4303, 17923, 75264, 316087, 1329006, 5592784, 23545716, 99155410, 417639459, 1759279887, 7411361169, 31223344768, 131544340291, 554206795807, 2334940230536, 9837444241610, 41446741048349, 174622202605439
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Row 2 of A239599

Examples

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

Formula

Empirical: a(n) = 8*a(n-1) -20*a(n-2) +34*a(n-3) -111*a(n-4) +174*a(n-5) -122*a(n-6) +518*a(n-7) -341*a(n-8) -675*a(n-9) -1185*a(n-10) -967*a(n-11) +4025*a(n-12) +4959*a(n-13) +4034*a(n-14) -3986*a(n-15) -19979*a(n-16) -8427*a(n-17) -7967*a(n-18) +26414*a(n-19) +23797*a(n-20) +16119*a(n-21) +20898*a(n-22) -32421*a(n-23) -3129*a(n-24) -50644*a(n-25) -27518*a(n-26) +3200*a(n-27) -2410*a(n-28) +25372*a(n-29) +8923*a(n-30) +10252*a(n-31) +12108*a(n-32) +1635*a(n-33) -1564*a(n-34) +436*a(n-35) -2746*a(n-36) -436*a(n-37) +368*a(n-38) -998*a(n-39) -486*a(n-40) -227*a(n-41) -151*a(n-42) -21*a(n-43) -4*a(n-44) for n>47

A239601 Number of 3Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 4, 31, 187, 1310, 9806, 76769, 611126, 4929897, 39990616, 325367130, 2651480323, 21625911002, 176464323565, 1440276473432, 11756877845964, 95977420564389, 783542978550992, 6396841387070227, 52224370266137630, 426366892135459667
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Row 3 of A239599

Examples

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

A239602 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

7, 4, 82, 643, 8773, 128347, 1991329, 31686730, 510551001, 8269184568, 134276229983, 2183190483244, 35519217176984, 578060604385531, 9409214132537899, 153168259416071355, 2493459020526521679
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Row 4 of A239599

Examples

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

A239593 Number of n X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 3, 31, 643, 38824, 12509870, 11135057785
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Diagonal of A239599

Examples

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

A239598 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

132, 1030, 9806, 128347, 1031560, 12509870, 120511910, 1104844380, 13122377637, 109004201919, 1143690420236, 11250183216347, 92332830515639
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Column 6 of A239599

Examples

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

A239603 Number of 5Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

10, 5, 177, 1737, 38824, 1031560, 30460289, 944810972, 30050150163, 966702472795
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2014

Keywords

Comments

Row 5 of A239599

Examples

			Some solutions for n=4
..3..0..0..0....2..0..0..0....3..2..2..0....3..0..2..0....2..3..2..2
..3..2..3..3....2..0..0..0....2..1..0..2....3..2..2..2....2..1..2..0
..2..1..1..3....3..2..2..0....3..2..0..2....2..1..0..0....3..2..2..0
..3..2..2..0....2..1..0..2....2..1..0..0....3..2..2..0....2..1..0..0
..2..1..2..0....3..2..0..0....2..0..0..3....3..1..2..0....3..2..0..2
		
Showing 1-10 of 10 results.