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

A264622 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

0, 1, 2, 1, 1, 4, 6, 5, 7, 15, 21, 23, 34, 58, 80, 101, 149, 230, 319, 431, 629, 928, 1299, 1810, 2617, 3784, 5336, 7536, 10828, 15521, 21992, 31236, 44713, 63862, 90741, 129177, 184524, 263178, 374521, 533619, 761403, 1085401, 1545839, 2203162
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Examples

			All solutions for n=4:
..1..5
..3..0
..8..2
..7..4
..9..6

Links

Crossrefs

Column 1 of A264628.

Formula

Empirical: a(n) = a(n-3) + 2*a(n-4) + a(n-5).
Empirical g.f.: x^2*(1 + x)^2 / (1 - x^3 - 2*x^4 - x^5). - Colin Barker, Jan 08 2019

A264623 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

0, 4, 13, 22, 61, 280, 832, 2373, 7225, 24371, 74664, 229729, 715055, 2264780, 7040309, 21916773, 68434305, 214187227, 668160424, 2084764226, 6510150515, 20333712284, 63475055481, 198151996889, 618702544012, 1931805153845
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Column 3 of A264628.

Examples

			Some solutions for n=4
..1..9..3..7....4..2..3..7....1..2..3..7....1..2..3.11....1..2..3.11
..5..0.10..2...12..0..1.11....5..0.10.15...12..0..7.15....5..0..7.15
.12..4.11..6....9.10..5..6....9..4.11..6...16..4..5..6...16..4.18..6
.16..8.15.19...16..8.15.19...16..8.18.19...13..8..9.10...13..8..9.10
.17.18.13.14...17.18.13.14...17.12.13.14...17.18.19.14...17.12.19.14

Links

Crossrefs

Cf. A264628.

Formula

Empirical: a(n) = 6*a(n-2) +10*a(n-3) +33*a(n-4) -5*a(n-5) -175*a(n-6) -235*a(n-7) -281*a(n-8) +137*a(n-9) +1360*a(n-10) +1709*a(n-11) +923*a(n-12) -602*a(n-13) -3180*a(n-14) -4831*a(n-15) -3269*a(n-16) +499*a(n-17) +3130*a(n-18) +4030*a(n-19) +4286*a(n-20) +2250*a(n-21) -653*a(n-22) -816*a(n-23) -617*a(n-24) -1339*a(n-25) -1262*a(n-26) -109*a(n-27) +234*a(n-28) -419*a(n-29) -307*a(n-30) +265*a(n-31) +234*a(n-32) +80*a(n-33) -114*a(n-34) +69*a(n-35) +143*a(n-36) -99*a(n-37) -22*a(n-38) +28*a(n-39) +11*a(n-40) -9*a(n-41) -14*a(n-42) +15*a(n-43) -6*a(n-44) +a(n-45)

A264624 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

0, 9, 40, 108, 660, 4032, 19521, 89469, 449550, 2308554, 11454129, 56190429, 279105021, 1393420077, 6924459960, 34329680172, 170475275106, 847412314182, 4209930190557, 20905557159789, 103832641922175, 515806878937563
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Column 4 of A264628.

Examples

			Some solutions for n=4
..5..2..3..4.14....5..2..3..4.14....5.11..3..4..9....5..2..3..4.14
..6..0..1..9.19....6..0..1..9.19....6..0..1..2.14....6..0..1..9.19
.15.16.17..7..8...11.16.13..7..8...20.12.17..7..8...15.12.13..7..8
.20.10.11.12.13...20.10.22.12.24...16.10.22.19.13...20.10.11.23.24
.21.22.23.24.18...21.15.23.17.18...21.15.23.24.18...21.22.16.17.18

Links

Crossrefs

Cf. A264628.

Formula

Empirical: a(n) = 3*a(n-1) +36*a(n-3) +108*a(n-4) -36*a(n-5) -351*a(n-6) -1863*a(n-7) -4698*a(n-8) -4050*a(n-9) -243*a(n-10) +729*a(n-11) for n>12

A264625 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

1, 16, 125, 684, 6107, 50353, 389512, 2986345, 23242594, 180618759, 1398264355, 10812994324, 83643299587, 647109775660, 5005530115866, 38711077685117, 299366137555908, 2315200537592902, 17904968501964924, 138466589997944123
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Column 5 of A264628.

Examples

			Some solutions for n=4
..1..2..8..4..5.11....6..2..3..4..5.17....6..2..8..4..5.11....6..2..3..9..5.11
.18..0.20.10..3.17...18..0..1.15.11.23...12..0..1.15..3.17...12..0..1.15.16..4
.13..6..7.27..9.23...13.14..7..8..9.10...13.19..7.16..9.10...13.14..7..8.17.10
.24.12.21.14.15.16...24.12.21.27.28.16...24.20.26.14.23.29...24.20.26.27.23.29
.25.26.19.28.29.22...25.26.19.20.29.22...25.18.27.28.21.22...25.18.19.28.21.22

Links

Crossrefs

Cf. A264628.

A264626 Number of (n+1) X (6+1) arrays of permutations of 0..n*7+6 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

0, 37, 393, 2736, 37225, 604916, 7201068, 81028312, 992539392, 12531858912, 152233949504, 1825908062080, 22176607035392, 270645955787776, 3285536600205312, 39798931437072384, 482959453126127616
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Column 6 of A264628.

Examples

			Some solutions for n=4
..1..2..3..4..5..6.20....7..2.16.10..5..6.13....1.15..9..4.11..6.13
..8..0.16.11.12.13.27....8..0..1.11..3..4.27....8..0.16..2..3.19..5
.15..7.23..9.10.33.34...15.22.30..9.32.20.12...21..7.17.18.10.20.12
.28.14.30.31.17.18.19...28.14.24.25.17.18.19...28.14.24.31.32.27.34
.29.21.22.32.24.25.26...29.21.31.23.33.34.26...29.30.22.23.33.25.26

Links

Crossrefs

Cf. A264628.

A264627 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

0, 76, 1200, 13556, 349391, 7907841, 145801320, 2739867178, 54011094032, 1041910674136, 19735900374844, 375966942137013, 7191151172715700, 137027122103977880, 2605652234584032150, 49595770201824007656
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Column 7 of A264628.

Examples

			Some solutions for n=4
.16.17..3.11.12..6..7.15....1.17..3.11.12..6..7.15....1..2..3..4..5..6..7.23
..9..0..1..2.28..4..5.23...24..0.26..2.13..4..5.31....9..0.26.27.13.14.15.31
.32..8.34.10.21.22.13.14...32..8..9.10.28.29.23.14...32..8.34.10.11.12.38.39
.25.26.27.18.19.20.31.39...25.16.27.18.19.20.21.22...25.16.17.18.19.20.21.22
.33.24.35.36.37.38.29.30...33.34.35.36.37.38.39.30...33.24.35.36.37.28.29.30

Links

Crossrefs

Cf. A264628.

A264629 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

1, 2, 4, 9, 16, 37, 76, 160, 337, 704, 1485, 3110, 6532, 13713, 28784, 60441, 126872, 266368, 559201, 1173968, 2464617, 5174122, 10862468, 22804377, 47874976, 100507613, 211003236, 442975264, 929971633, 1952360368, 4098738901
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Examples

			Some solutions for n=4:
..1..6..3..4..9....1..6..7..4..9...10..2.12..4.14....5..2..7..4..9
.10..0.12..2.14...10..0.12..2..3....6..0..1..9..3...10..0..1.13..3
.11..5.13..7..8...11..5.13.14..8...11..5.13..7..8...11.12..6.14..8

Links

Crossrefs

Row 2 of A264628.

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-5) - 2*a(n-6) + 4*a(n-7) - a(n-10).
Empirical g.f.: x*(1 + x^3 - 2*x^4 + 3*x^5 - x^8) / (1 - 2*x - 2*x^5 + 2*x^6 - 4*x^7 + x^10). - Colin Barker, Jan 08 2019

A264630 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

2, 4, 13, 40, 125, 393, 1200, 3759, 11572, 36004, 111380, 345489, 1070564, 3318409, 10285305, 31878944, 98808901, 306255436, 949236490, 2942139012, 9119124333, 28264569620, 87605626309, 271532263929, 841610129904, 2608557687707
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Row 3 of A264628.

Examples

			Some solutions for n=4
..1.11..7..4..9....1..2..7..4..9....5.11..3..4..9....1.11..3..4..9
..6..0..8..2..3...10..0.12.18..3....6..0..1..2.14...10..0..8..2.14
.15..5.17.14.19...15..5..6.14..8...15.12.17..7..8...15..5..6..7.19
.16.10.18.12.13...16.17.11.19.13...16.10.18.19.13...16.17.18.12.13

Links

Crossrefs

Cf. A264628.

Formula

Empirical: a(n) = 6*a(n-2) +10*a(n-3) +4*a(n-4) -2*a(n-5) -a(n-6) +4*a(n-7) +18*a(n-8) +25*a(n-9) -8*a(n-10) -6*a(n-11) -10*a(n-12) +a(n-15)

A264631 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

1, 8, 22, 108, 684, 2736, 13556, 68972, 316068, 1534532, 7430832, 35311040, 170094764, 817176616, 3914397580, 18804795120, 90252696296, 433011737840, 2078662232124, 9975949817428, 47876003240128, 229786823307824
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Row 4 of A264628.

Examples

			Some solutions for n=4
..1.11..7..4..9....1..6..3..4..9....1..2..3..4.14....1..2.12..4.14
..6..0.12..2..3...10..0..8..2.14...15..0.17..9.19....6..0..8..9..3
.20..5.13.14..8...20..5.22..7.19...20..5..6..7..8...15..5.13..7.19
.16.10.22.19.24...16.17.11.12.13...16.10.11.12.13...20.10.11.23.24
.21.15.23.17.18...21.15.23.24.18...21.22.23.24.18...21.22.16.17.18

Links

Crossrefs

Cf. A264628.

Formula

Empirical: a(n) = 3*a(n-1) +36*a(n-3) -18*a(n-4) +186*a(n-5) +83*a(n-6) +144*a(n-7) +684*a(n-8) -1872*a(n-9) +508*a(n-10) -5048*a(n-11) -3240*a(n-12) +720*a(n-13) -95040*a(n-14) +3072*a(n-15) +3456*a(n-16) +13824*a(n-18) for n>21

A264632 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

Original entry on oeis.org

1, 16, 61, 660, 6107, 37225, 349391, 2557552, 19278771, 156296532, 1179331101, 9153019452, 71351814352, 548547053971, 4256314971079, 32951502011481, 254689445056816, 1972727580974503, 15263452717088948, 118105432842264754
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Row 5 of A264628.

Examples

			Some solutions for n=4
..5..2..3..4..9....1..6..3..4..9....1..2.12..4.14....5..6..7..4..9
.10..0..1.13.14...10..0.12..2.14....6..0.17..9..3...10..0..1..2..3
.11.12..6..7..8...11..5.13..7..8...11..5.13..7..8...15.12.13.14..8
.16.21.18.19.24...16.17.22.19.24...16.10.22.19.24...16.17.11.19.24
.25.15.27.17.29...25.15.27.28.18...25.15.27.28.18...25.22.27.28.18
.26.20.28.22.23...26.20.21.29.23...26.20.21.29.23...26.20.21.29.23

Links

Crossrefs

Cf. A264628.
Showing 1-10 of 13 results. Next

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