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 13 results. Next

A241429 Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero 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, 5, 2, 3, 5, 6, 9, 10, 15, 21, 28, 38, 49, 67, 91, 122, 169, 226, 312, 423, 578, 791, 1075, 1471, 2003, 2732, 3731, 5080, 6941, 9457, 12908, 17609, 24015, 32776, 44699, 60991, 83206, 113499, 154866, 211239, 288211, 393168, 536370, 731761, 998249, 1361895
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Examples

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

Crossrefs

Column 2 of A241435.

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + a(n-7) + a(n-8) - 2*a(n-9) + 2*a(n-10) - a(n-11) for n>13.
Empirical g.f.: x*(3 - x - 8*x^2 + 5*x^3 + 6*x^4 - 8*x^5 + 2*x^6 + 4*x^7 - 5*x^8 + 3*x^9 - 6*x^11 + 4*x^12) / ((1 - x)*(1 - x - x^2 + x^3 - x^5 + x^6 - x^8 + x^9 - x^10)). - Colin Barker, Oct 30 2018

A241430 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero 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, 10, 22, 97, 213, 381, 1005, 1900, 4137, 10518, 21092, 47994, 111034, 227786, 526558, 1173266, 2506934, 5760387, 12607288, 27523425, 62352333, 135931174, 300820619, 674058895, 1474383381, 3279987103, 7290574867, 16018404203
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Column 3 of A241435

Examples

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

A241431 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero 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, 21, 74, 515, 1527, 5304, 20690, 61348, 257119, 920918, 3090540, 12030044, 40508800, 149637207, 549347596, 1879652737, 7032173983, 24856568624, 88496458840, 325227255990, 1142461364583, 4148471540343, 14938347230115
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Column 4 of A241435

Examples

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

A241432 Number of nX5 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero 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, 45, 158, 1563, 7495, 37148, 218885, 1059975, 7257895, 44141371, 244603126, 1599162188, 8958092747, 55332407751, 336911717484, 1937285923500, 12085963190320, 70661956336398, 424547431732947, 2581132242865135
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Column 5 of A241435

Examples

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

A241436 Number of 2Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or zero 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, 5, 10, 21, 45, 88, 181, 378, 710, 1460, 2973, 5668, 11567, 23202, 45182, 91386, 182056, 358886, 721278, 1433814, 2843343, 5691577, 11312714, 22494505, 44919750, 89325211, 177819368, 354608529, 705515901, 1405063399, 2799954077, 5572860402
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Row 2 of A241435

Examples

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

Formula

Empirical: a(n) = 2*a(n-2) +8*a(n-3) -a(n-4) -10*a(n-5) -18*a(n-6) +8*a(n-7) +20*a(n-8) +20*a(n-9) -24*a(n-10) -22*a(n-11) -a(n-12) +32*a(n-13) +8*a(n-14) -3*a(n-15) -12*a(n-16) +4*a(n-17) -5*a(n-18) -4*a(n-20) -3*a(n-21) +2*a(n-22) for n>24

A241437 Number of 3 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or zero 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, 2, 22, 74, 158, 448, 1272, 3284, 8331, 23365, 63819, 159963, 450553, 1178189, 3085252, 8574583, 21981254, 59397292, 161093107, 416692229, 1133829778, 3023012096, 7951525097, 21508340343, 56988406704, 151552827477, 406957891025
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Row 3 of A241435.

Examples

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

Crossrefs

Cf. A241435.

A241438 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or zero 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, 3, 97, 515, 1563, 5915, 22712, 76145, 270960, 1073158, 3818620, 13721807, 51728838, 187790119, 699951598, 2604140270, 9348611449, 35299653581, 130303556135, 471759570058, 1773938926867, 6503523325619, 23881500761462
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Row 4 of A241435

Examples

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

A241428 Number of n X n 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or zero 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, 5, 22, 515, 7495, 377314, 79901137, 34796682706
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Diagonal of A241435

Examples

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

A241433 Number of nX6 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero 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

15, 88, 448, 5915, 45139, 377314, 4136727, 34541924, 418453966, 4088141292, 40962255699, 430943324954, 4031664281839
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Column 6 of A241435

Examples

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

A241434 Number of nX7 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero 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, 181, 1272, 22712, 282527, 4122537, 79901137, 1231102996, 26880310825, 446955799466
Offset: 1

Views

Author

R. H. Hardin, Apr 22 2014

Keywords

Comments

Column 7 of A241435

Examples

			Some solutions for n=3
..3..3..2..2..2..3..2....2..2..3..2..3..3..2....3..3..2..2..2..3..2
..2..1..2..1..1..1..0....2..1..1..2..1..1..2....2..1..2..0..1..1..2
..3..3..2..2..2..2..0....3..3..0..2..2..0..2....3..3..2..2..1..2..0
		
Showing 1-10 of 13 results. Next