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 1-3 of 3 results.

A113163 a(n) = binomial(5, n) * binomial(7, 5-n).

Original entry on oeis.org

21, 175, 350, 210, 35, 1
Offset: 0

Views

Author

Zerinvary Lajos, Jan 05 2006

Keywords

Comments

The sequence sums to binomial(12, 5).

Crossrefs

Cf. A113162.

Programs

  • Mathematica
    Table[Binomial[5,n]Binomial[7,5-n],{n,0,5}] (* Harvey P. Dale, Feb 19 2023 *)

Extensions

Edited by Don Reble, Jan 26 2006

A113164 a(n) = binomial(6, n)^2.

Original entry on oeis.org

1, 36, 225, 400, 225, 36, 1
Offset: 0

Views

Author

Zerinvary Lajos, Jan 05 2006

Keywords

Comments

The sequence sums to binomial(12, 6).

Crossrefs

Cf. A008459, A113162.

Extensions

Edited by Don Reble, Jan 26 2006

A113899 Number parallelogram based on Pascal's triangle (and special mirror of central and multiply of diagonal).

Original entry on oeis.org

252, 126, 126, 56, 140, 56, 21, 105, 105, 21, 6, 60, 120, 60, 6, 1, 25, 100, 100, 25, 1, 6, 60, 120, 60, 6, 21, 105, 105, 21, 56, 140, 56, 126, 126, 252
Offset: 0

Views

Author

Zerinvary Lajos, Jan 29 2006, May 28 2007

Keywords

Comments

.............................C(0,0)*C(10,5)
......................C(1,0)*C(9,5)...C(1,1)*C(9,4)
...............C(2,0)*C(8,5)...C(2,1)*C(8,4)...C(2,2)*C(8,3)
........C(3,0)*C(7,5)...C(3,1)*C(7,4)...C(3,2)*C(7,3)...C(3,3)*C(7,2)
...C(4,0)*C(6,5)...C(4,1)*C(6,4)...C(4,2)*C(6,3)...C(4,3)*C(8,2)...C(4,4)*C(6,1)
C(5,0)*C(5,5)...C(5,1)*C(5,4)...C(5,2)*C(5,3)...C(5,3)*C(5,2)...C(5,4)*C(5,1)...C(5,5)*C(5,0)
...C(6,1)*C(4,4)...C(4,1)*C(6,4)...C(4,2)*C(6,3)...C(4,3)*C(8,2)...C(6,5)*C(4,0)
........C(7,2)*C(3,3)...C(7,3)*C(3,2)...C(7,4)*C(3,1)...C(7,5)*C(3,0)
...............C(8,3)*C(2,2)...C(8,4)*C(2,1)...C(8,5)*C(2,0)
......................C(9,4)*C(1,1)...C(9,5)*C(1,0)
.............................C(10,5)*C(0,0)
"m" matching: analog (permutations with exactly "m" fixed points.
if aaaaabbbbb (a 5 letters b 5 letters) permutations compared aaaaaaaaaa (a 10 times letters) or compared bbbbbbbbbb (b 10 times letters then 252 "5" matching. ("5" matching: analog (permutations with exactly 5 fixed points.)
If aaaaabbbbb (a 5 letters b 5 letters) permutations compared aaaaabbbbb (a 5 times letters b 5 times letters)then 1 "0" matching), 25 "2"matching 100 "4" matching, 100 "6" matching, 25 "8" matching and 1 "10" matching.(A008459 formatted as a triangular array: 6.rows)
If aaaaabbbbb (a 5 letters b 5 letters) permutations compared abbbbbbbbb (a 1 times letters b 9 times letters) or aaaaaaaaab (a 9 times letters b 1 times letters) then 126 "4" and 126 "6" matching.
etc...
matching equivalent "fixed-point"
example:
arrangement relevant!
compared
letters
times
matching:0.....1.....2.....3.....4.....5.....6.....7.....8.....9.....10
compared.
letters..
times....
.a..b
10..0.................................252..............................
.9..1...........................126.........126........................
.8..2......................56.........140..........56..................
.7..3................21.........105.........105..........21............
.6..4..........6...........60.........120..........60..........6.......
.5..5....1...........25.........100.........100..........25...........1
.4..6..........6...........60.........120..........60..........6.......
.3..7................21.........105.........105..........21............
.2..8......................56.........140..........56..................
.1..9...........................126.........126........................
0..10..................................252.............................
matching.0.....1.....2.....3.....4.....5.....6.....7.....8.....9.....10
The Maple code produces
252, 126, 56, 21, 6, 1
126, 140, 105, 60, 25, 6
56, 105, 120, 100, 60, 21
21, 60, 100, 120, 105, 56
6, 25, 60, 105, 140, 126
1, 6, 21, 56, 126, 252
which is the table rotated right by Pi/4.

Crossrefs

Cf. A113162, A113163, A113164.

Programs

  • Maple
    for n from 0 to 5 do seq(binomial(i,n)*binomial(10-i,5-n), i=0+n..10-5+n ); # Zerinvary Lajos, Mar 31 2009
Showing 1-3 of 3 results.

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