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A113899 Number parallelogram based on Pascal's triangle (and special mirror of central and multiply of diagonal). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

LINKS

Table of n, a(n) for n=0..35.

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

CROSSREFS

Cf. A113162, A113163, A113164.

Sequence in context: A176377 A268848 A177809 * A045182 A046331 A066695

Adjacent sequences:  A113896 A113897 A113898 * A113900 A113901 A113902

KEYWORD

easy,fini,nonn,uned

AUTHOR

Zerinvary Lajos, Jan 29 2006, May 28 2007

STATUS

approved

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Last modified February 24 01:16 EST 2020. Contains 332195 sequences. (Running on oeis4.)