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

A264373 Number of (n+1)X(2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

2, 1, 13, 25, 128, 347, 1343, 4172, 14711, 48187, 164644, 549209, 1857120, 6231551, 21001218, 70602740, 237686843, 799548823, 2690789595, 9053237740, 30464275277, 102504319825, 344916282634, 1160576447091, 3905173385325, 13140236820844
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 2 of A264379.

Examples

			Some solutions for n=4
..1..2..3....1..4..3....3..2..5....3..4..5....3..4..5....1..4..3....1..4..3
..0..7..6....0..7..8....0..1..6....0..1..6....0..1..8....0..7..6....0..5..6
..9..4..5....2.10..5....7..4..9....2..8..9....2.10..9....2..8..5....2.10..9
.12.13.14....6.13.12...12.13.14...12..7.14....6..7.12...12.13.14...12..7..8
..8.10.11....9.14.11....8.10.11...13.10.11...13.14.11....9.10.11...13.14.11
		

Crossrefs

Cf. A264379.

Formula

Empirical: a(n) = a(n-1) +13*a(n-2) -4*a(n-3) -57*a(n-4) +11*a(n-5) +138*a(n-6) -25*a(n-7) -213*a(n-8) +38*a(n-9) +220*a(n-10) -26*a(n-11) -151*a(n-12) -7*a(n-13) +62*a(n-14) +19*a(n-15) -21*a(n-16) -8*a(n-17) +7*a(n-18) +a(n-19) -a(n-20)

A264374 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

4, 6, 80, 441, 3249, 22484, 156293, 1097881, 7657324, 53631087, 374971549, 2623479579, 18351250984, 128373536659, 898014323096, 6281872878413, 43943675806740, 307399346962192, 2150352679484064, 15042375439676549
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 3 of A264379.

Examples

			Some solutions for n=4
..4..2..6..5....4..2..6..5....1..2..4..7....1..2..3..5....1..5..6..7
..0..1.10..3....0..1..8.11....0..9.10..3....0..6..8..9....0..9..2..3
..9.13.11..7....9..3.12.13...12..5..6.13....4.10.11..7....4.10.11.13
..8.14.16.17...16..7.10.19....8.14.16.11...13.17.16.19....8.14.16.17
.12.18.19.15...17.18.14.15...17.18.19.15...12.18.14.15...12.18.19.15
		

Crossrefs

Cf. A264379.

Formula

Empirical: a(n) = 2*a(n-1) +58*a(n-2) -21*a(n-3) -1238*a(n-4) -137*a(n-5) +15288*a(n-6) +4560*a(n-7) -127006*a(n-8) -47282*a(n-9) +772066*a(n-10) +326725*a(n-11) -3602505*a(n-12) -1772071*a(n-13) +13317616*a(n-14) +7874851*a(n-15) -39927191*a(n-16) -28721785*a(n-17) +98667418*a(n-18) +85571362*a(n-19) -202707758*a(n-20) -208446136*a(n-21) +346194120*a(n-22) +417845725*a(n-23) -485816139*a(n-24) -693362865*a(n-25) +544797544*a(n-26) +951161517*a(n-27) -465400385*a(n-28) -1074696221*a(n-29) +273846246*a(n-30) +1005646712*a(n-31) -64145514*a(n-32) -794935940*a(n-33) -92496118*a(n-34) +530782727*a(n-35) +167673359*a(n-36) -287037779*a(n-37) -164313896*a(n-38) +113531703*a(n-39) +114897917*a(n-40) -21596495*a(n-41) -58034484*a(n-42) -7483588*a(n-43) +20885338*a(n-44) +8031702*a(n-45) -5392938*a(n-46) -3705501*a(n-47) +1026905*a(n-48) +1321563*a(n-49) -64616*a(n-50) -395895*a(n-51) -61769*a(n-52) +89081*a(n-53) +29582*a(n-54) -14918*a(n-55) -7198*a(n-56) +2444*a(n-57) +1572*a(n-58) -165*a(n-59) -174*a(n-60) +15*a(n-61) +14*a(n-62) -2*a(n-63) -a(n-64)

A264375 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

6, 9, 385, 3778, 63575, 828400, 11888603, 163298870, 2275569624, 31552306013, 437685392431, 6074696881202, 84245234781160, 1169032382776504, 16215316393763249, 224976383266144188, 3120908613452812544
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 4 of A264379.

Examples

			Some solutions for n=4
..5..2..3..6..9....5..2..3..4..7....1..2..3..8..7....5..6..7..8..9
..0..1.10.13..4....0..1.10.13.12....0.11.10.13..4....0..1.12.11..4
.11.12.15.16.17...15..6.17..8..9....5..6.15.14..9....2..3.13.16.17
..7..8.20.23.24...20.11.18.23.22...16.17.20.21.24...10.21.20.23.24
.21.22.14.18.19...21.16.14.24.19...12.22.23.18.19...15.22.14.18.19
		

Crossrefs

Cf. A264379.

A264376 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

9, 61, 2345, 60858, 1742881, 48714516, 1363452981, 38221084820, 1068788896516, 29927513269705, 837176817328453, 23429857747772820, 655532815387819189, 18343277111401479326, 513247057017765586701, 14361187855657149397556
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 5 of A264379.

Examples

			Some solutions for n=4
..6..2..3..7..8.11....1..2..3..7.10..9....6..2..8..7.10..9....6..7..8..4.10..9
..0..1.12.10..4.15....0.13.12.15..4..5....0..1.12.13..4..5....0..1.14..3.16.15
.13.19.18..5.17.21....6.14.18.21.17.11...18..3.15.21.17.11....2.19.18..5.17.11
.24..9.14.27.16.29....8.20.24.22.26.27...24.25.26.22.16.27...12.13.24.27.28.29
.25.26.20.28.22.23...25.19.16.28.29.23...14.19.20.28.29.23...25.26.20.21.22.23
		

Crossrefs

Cf. A264379.

A264377 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

15, 121, 14329, 711068, 45132986, 2546661201, 149731056598, 8620411258657, 499872831041401, 28871184063697655, 1669447411395132846, 96462826329498703173, 5574683427373667949652, 322122388885074528092794
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 6 of A264379.

Examples

			Some solutions for n=3
..7..2..3..4..5.12.11....7..2..3..8..5.12.13....7..2..9..8..5.10.13
..0..1.10.17.18.13..6....0..1.14.11..4.17.18....0..1.16..3..4.17.18
.21..8..9.22.23.24.27...15.22.21.10..6.24.27...15.22.21.24..6.12.27
.14.15.16.25.26.19.20....9.23.16.25.26.19.20...14.23.11.25.26.19.20
		

Crossrefs

Cf. A264379.

A264378 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

25, 544, 88264, 9407584, 1187897216, 135926940964, 16353452350876, 1906883090233889, 225710195773223581, 26480802739477668891, 3118944367808136172136, 366509498887083495949171
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 7 of A264379.

Examples

			Some solutions for n=3
..8..9.10..4..5..6.12.13....8..2..3..9.10..6.14.13....8..2..3..4.10.11..7.15
..0..1..2..3.18.14.20.21....0..1.11.12..4..5.15..7....0..1.16.19.18..5.22.21
.24.25.26.11.28..7.30.31...24.25.26.20.28.27.30.31...17..9.24.20..6.27.28.29
.16.17.27.19.29.15.22.23...16.17.18.19.29.21.22.23...25.26.12.13.14.30.31.23
		

Crossrefs

Cf. A264379.

A264380 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

0, 1, 6, 9, 61, 121, 544, 1357, 5100, 14340, 49324, 147230, 485141, 1491460, 4812843, 15012153, 47950974, 150636184, 478755674, 1509249756, 4785018013, 15110309428, 47849311565, 151226992088, 478604645313, 1513243349293, 4787751445331
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Examples

			Some solutions for n=4:
..1..6..5..4..7....1..2..3..8..7....5..6..3..8..7....5..2..3..8..7
..0.11.10..3.14....0.11.10.13.12....0..1.10.11..4....0..1.10.13.12
..2.12.13..8..9....5..6..4.14..9....2.12.13.14..9...11..6..4.14..9
		

Crossrefs

Row 2 of A264379.

Formula

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) + 7*a(n-4) - 4*a(n-5) - a(n-6) + 5*a(n-7) - 4*a(n-8) + 2*a(n-9) - a(n-10).
Empirical g.f.: x^2*(1 + 4*x - 8*x^2 + 19*x^3 - 17*x^4 + 13*x^5 - 8*x^6 + 2*x^7 - x^8) / (1 - 2*x - 5*x^2 + 6*x^3 - 7*x^4 + 4*x^5 + x^6 - 5*x^7 + 4*x^8 - 2*x^9 + x^10). - Colin Barker, Jan 07 2019

A264381 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 13, 80, 385, 2345, 14329, 88264, 538417, 3284212, 20034334, 122324128, 746763789, 4557854384, 27820780958, 169811407936, 1036520322168, 6326740063001, 38617694163183, 235716525841304, 1438783215929873
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Row 3 of A264379.

Examples

			Some solutions for n=4
..1..6..5..8..7....1..2..5..4..9....5..2..7..4..9....5..2..3..8..7
..0.11..2.13.12....0..7..8..3.12....0..1..8..3.12....0..1.12..9..4
.15..3..4.16..9...15..6.17.16.19...15..6.13.16.17...15..6.13.16.17
.10.17.18.19.14...10.11.18.13.14...10.11.18.19.14...10.11.18.19.14
		

Crossrefs

Cf. A264379.

Formula

Empirical recurrence of order 70 (see link above)

A264382 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

0, 25, 441, 3778, 60858, 711068, 9407584, 115929779, 1485398475, 18746069596, 237937556367, 3012183685044, 38165904080061, 483579364451792, 6125734123144467, 77617437527388938, 983250878745280550
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Row 4 of A264379.

Examples

			Some solutions for n=4
..1..6..5..8..9....1..2..7..6..9....5..6..7..8..9....1..6..3..4..7
..0.11.12.13..4....0.11.10..3..4....0..1.10..3..4....0.11..2.13.14
..2..3..7.18.17....5.16.15..8.17....2.12.15.18.17....5.12.15.18..9
.10.21.20.23.22...20.21.18.13.14...16.11.20.13.14...10..8.20.23.22
.15.16.14.24.19...12.22.23.24.19...21.22.23.24.19...21.16.17.24.19
		

Crossrefs

Cf. A264379.

Formula

Empirical recurrence of order 81 (see link above)

A264383 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 128, 3249, 63575, 1742881, 45132986, 1187897216, 30373276651, 792780331712, 20444262438305, 530521904672461, 13716515010894393, 355463297798764953, 9199078922790223336, 238250431643039032101, 6167702521336260154448
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Row 5 of A264379.

Examples

			Some solutions for n=4
..5..2..3..4..9....1..2..3..6..7....1..6..5..4..7....5..2..3..4..9
..0..1.10.11.12....0.11..8..9..4....0.11.10..9.12....0..1.10.11.12
.15..6..7..8.19....5.12.15.14.19....2..3.15.18.17...15..6.13.18.19
.20.21.22.13.14...10.17.18.13.22...16..8.22.19.14....7..8.20.21.22
.25.16.17.18.29...21.16.25.26.29...25.13.27.26.29...25.16.14.26.29
.26.27.28.23.24...20.27.28.23.24...20.21.28.23.24...17.27.28.23.24
		

Crossrefs

Cf. A264379.
Showing 1-10 of 13 results. Next