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.

A201066 Number of nX2 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

21, 70, 35, 77, 749, 972, 127, 3034, 7161, 2170, 3258, 24178, 22584, 1925, 44526, 93370, 24434, 32166, 212694, 174093, 12492, 282808, 559380, 136472, 168016, 1042800, 794792, 51945, 1159645, 2215350, 518715, 613149, 3656445, 2665100
Offset: 1

Views

Author

R. H. Hardin Nov 26 2011

Keywords

Comments

Column 2 of A201072

Examples

			Some solutions for n=10
..0..3....0..1....0..2....0..0....0..0....0..0....0..1....0..0....0..1....0..1
..0..3....0..3....0..2....0..1....0..1....1..2....0..1....0..2....0..1....0..1
..0..4....1..3....1..3....1..2....1..3....1..2....0..3....1..2....0..2....0..2
..1..4....1..3....1..3....1..2....2..3....1..3....1..4....1..2....1..2....1..2
..1..4....2..4....1..3....3..3....2..3....2..4....2..4....3..5....2..3....2..4
..1..5....2..4....2..4....3..5....2..4....3..4....2..4....3..5....3..3....3..4
..2..5....2..4....4..5....4..5....4..5....3..5....3..5....3..5....4..4....3..5
..2..5....5..6....4..5....4..5....4..5....4..6....3..5....4..6....5..6....3..5
..2..6....5..6....5..6....4..6....5..6....5..6....5..6....4..6....5..6....5..6
..6..6....5..6....6..6....6..6....6..6....5..6....6..6....4..6....5..6....6..6

Links

Formula

Empirical: a(n) = 7*a(n-7) -21*a(n-14) +35*a(n-21) -35*a(n-28) +21*a(n-35) -7*a(n-42) +a(n-49)
Subsequences for n modulo 7 = 1,2,3,4,5,6,0
p=(n+6)/7: a(n) = (5887/60)*p^6 - (799/6)*p^5 + (287/4)*p^4 - (52/3)*p^3 + (49/30)*p^2
q=(n+5)/7: a(n) = (5887/36)*q^6 - (673/6)*q^5 + (151/9)*q^4 + (13/6)*q^3 - (11/36)*q^2
r=(n+4)/7: a(n) = (5887/180)*r^6 + (5/2)*r^5 - (7/36)*r^4 - (1/90)*r^2
s=(n+3)/7: a(n) = (5887/180)*s^6 + (458/15)*s^5 + (365/36)*s^4 + (17/6)*s^3 + (59/90)*s^2 + (2/15)*s
t=(n+2)/7: a(n) = (5887/36)*t^6 + (925/3)*t^5 + (7489/36)*t^4 + (121/2)*t^3 + (143/18)*t^2 + (2/3)*t
u=(n+1)/7: a(n) = (5887/60)*u^6 + (862/3)*u^5 + (4007/12)*u^4 + (1153/6)*u^3 + (817/15)*u^2 + 6*u
v=(n+0)/7: a(n) = (841/180)*v^6 + (101/5)*v^5 + (1325/36)*v^4 + (73/2)*v^3 + (946/45)*v^2 + (34/5)*v + 1

A201067 Number of nX3 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

35, 35, 514, 2611, 3937, 50334, 4448, 381982, 206357, 1377351, 2831603, 1974341, 20355511, 1239614, 73355614, 25640082, 134750988, 236836508, 134563397, 1068791444, 49395188, 2697358626, 852508061, 3859642876, 5707775509
Offset: 1

Views

Author

R. H. Hardin Nov 26 2011

Keywords

Comments

Column 3 of A201072

Examples

			Some solutions for n=7
..0..0..3....0..1..3....0..0..0....0..0..2....0..0..0....0..1..1....0..0..1
..0..1..4....0..2..3....1..1..2....0..1..2....1..2..5....0..2..3....0..2..3
..1..1..4....0..2..4....1..2..2....1..1..4....1..3..5....0..2..4....1..2..3
..2..3..4....1..2..5....3..3..5....2..3..5....1..3..5....1..2..5....1..3..4
..2..3..5....1..3..6....3..4..5....3..3..6....2..3..6....3..3..6....2..4..5
..2..5..5....4..5..6....4..5..6....4..5..6....2..4..6....4..4..6....4..5..5
..6..6..6....4..5..6....4..6..6....4..5..6....4..4..6....5..5..6....6..6..6

Links

A201068 Number of nX4 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

35, 77, 2611, 22440, 43308, 1127514, 175865, 20393189, 14766300, 158314010, 495900141, 452698962, 6176064188, 493804760, 39573007249, 18657025428, 128820947525, 280570465208, 193035367346, 1994641001437, 119475251989
Offset: 1

Views

Author

R. H. Hardin Nov 26 2011

Keywords

Comments

Column 4 of A201072

Examples

			Some solutions for n=5
..0..1..3..4....0..0..1..2....0..0..2..3....0..1..1..3....0..0..2..3
..0..2..3..4....0..1..3..4....0..2..3..5....0..2..2..3....0..1..3..4
..1..2..4..5....1..2..4..5....1..2..4..5....0..4..5..5....1..2..3..5
..1..2..5..6....2..3..4..5....1..3..4..5....1..4..5..6....1..4..4..6
..3..5..6..6....3..6..6..6....1..6..6..6....2..4..6..6....5..5..6..6

Links

A201069 Number of n X 5 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

21, 749, 3937, 43308, 2250982, 11512566, 3558888, 473983329, 4102010820, 3773723044, 16952125989, 322374164226, 702125798925, 118364239437, 7609460886830, 38642046123073, 22788500587323, 61246570410530
Offset: 1

Views

Author

R. H. Hardin Nov 26 2011

Keywords

Comments

Column 5 of A201072.

Examples

			Some solutions for n=4
..0..0..1..2..2....0..0..1..2..5....0..1..2..2..4....0..0..0..1..2
..0..1..2..3..3....0..1..3..3..5....0..1..3..4..6....1..2..3..3..3
..1..3..4..4..6....1..2..4..4..6....0..1..3..4..6....1..4..4..4..6
..5..5..5..6..6....2..3..4..6..6....3..5..5..5..6....2..5..5..6..6

Links

A201071 Number of n X 7 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 127, 4448, 175865, 3558888, 76714325, 1001060834, 13053459189, 126679336122, 1146503112430, 8486668894331, 60373612028710, 361132659179512
Offset: 1

Views

Author

R. H. Hardin, Nov 26 2011

Keywords

Comments

Column 7 of A201072.

Examples

			Some solutions for n=3
..0..0..0..1..2..3..5....0..1..1..2..2..3..3....0..0..1..1..1..2..5
..1..2..2..3..3..5..5....0..1..2..3..4..5..5....0..2..2..3..3..4..6
..1..4..4..4..6..6..6....0..4..4..5..6..6..6....3..4..4..5..5..6..6

Crossrefs

Cf. A201072.

A201065 Number of n X n 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

7, 70, 514, 22440, 2250982, 45244488, 1001060834, 1438433201164
Offset: 1

Views

Author

R. H. Hardin Nov 26 2011

Keywords

Comments

Diagonal of A201072.

Examples

			Some solutions for n=4
..0..0..2..2....0..1..1..1....0..0..3..3....0..1..1..3....0..0..3..3
..1..1..4..4....0..2..2..4....0..2..3..4....0..2..4..6....0..2..4..4
..1..3..5..6....3..3..4..5....1..2..5..6....1..2..4..6....1..2..5..6
..3..5..5..6....5..6..6..6....1..4..5..6....3..5..5..6....1..3..5..6

Crossrefs

Cf. A201072.

A201070 Number of nX6 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

7, 972, 50334, 1127514, 11512566, 45244488, 76714325, 4070916182, 93433967419, 1001816580924, 5795448454236, 18395210387740, 28907664595262, 18988731471112, 524722518340932
Offset: 1

Views

Author

R. H. Hardin Nov 26 2011

Keywords

Comments

Column 6 of A201072

Examples

			Some solutions for n=3
..0..0..1..2..3..5....0..1..1..1..3..3....0..0..1..2..3..4....0..0..1..1..2..4
..1..2..3..4..4..6....0..2..3..4..5..6....0..1..3..3..5..5....0..3..3..4..5..5
..1..2..4..5..5..6....2..2..4..5..5..6....2..2..4..6..6..6....2..4..5..6..6..6
Showing 1-7 of 7 results.

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