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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 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 A330616 A046331 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 March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)