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 A129536 Number parallelogram based on Pascal's triangle (and special mirror of central and multiply of diagonal). 0
 45, 9, 36, 1, 16, 28, 3, 21, 21, 6, 24, 15, 10, 25, 10, 15, 24, 6, 21, 21, 3, 28, 16, 1, 36, 9, 45 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sequence arrangement: ....................C(10,2)*C(0,0) .............C(9,1)*C(1,1)...C(9,2)*C(1,0) .....C(8,0)*C(2,2)...C(8,1)*C(2,1)...C(8,2)*C(2,0) ..............C(7,0)*C(3,2)...C(7,1)*C(3,1)...C(7,2)*C(3,0) .....................C(6,0)*C(4,2)...C(6,1)*C(4,1)...C(6,2)*C(4,0) .............................C(5,0)*C(5,2)...C(5,1)*C(5,1)...C(5,2)*C(5,0) .....................................C(4,0)*C(6,2)...C(4,1)*C(6,1)...C(4,2)*C(6,0) .............................................C(3,0)*C(7,2)...C(3,1)*C(7,1)...C(3,2)*C(7,0) .....................................................C(2,0)*C(8,2)...C(2,1)*C(8,1)...C(2,2)*C(8,0) .............................................................C(1,0)*C(9,2)...C(1,1)*C(9,1) .....................................................................C(0,0)*C(10,2) "m" matching: analog (permutations with exactly "m" fixed points. if aabbbbbbbb (a twice letters b 8 times letters) permutations compared aaaaaaaaaa (a 10 times letters) then 45 * "2" matching.(sum 45)("2" matching: analog(permutations with exactly 2 fixed points.) if compared bbbbbbbbbb (b 10 times letters then 45 * "8" matching.(sum 45) ("8" matching: analog (permutations with exactly 8 fixed points.). If aabbbbbbbb (a 2 letters b 8 letters) permutations compared aabbbbbbbb (a twice letters b 8 times letters)then 1 * "10" matching),16 * "8" matching, 28 * "6" matching (sum 45) If aabbbbbbbb (a 8 letters b 2 letters)permutations compared aaaaaaaabb (a 8 times letters b twice letters)then 1 * "0" matching),16 * "2" matching, 28 * "4" matching (sum 45) all rows (sum 45) etc... matching equialent or analog "fixed points" example: arrangement relevant! compared letters.. times.... a...b matching:..........0..1..2..3..4..5..6..7..8..9..10 0..10...................45......................... .1..9.................9....36...................... .2..8..............1.....16....28.................. .3..7.................3....21.....21................ .4..6....................6....24....15............ .5..5......................10....25.....10......... .6..4.........................15....24.....6........ .7..3.............................21....21.....3.... .8..2................................28....16......1 .9..1...................................36.....9.... 10..0......................................45....... matching:...........0..1..2..3..4..5..6..7..8..9..10 The Maple code produces this: 45, 36, 28, 21, 15, 10, 6, 3, 1 9, 16, 21, 24, 25, 24, 21, 16, 9 1, 3, 6, 10, 15, 21, 28, 36, 45 This is the table rotated right by Pi/4. LINKS Lottery Numeric Positional Frequency Charts Note:Information herein is intended for lottery system developers, analysts and operators. It is not intended for gaming purposes. 3/11 table: (Horizontal > Total: 165, Vertical > Total: 45) [From Zerinvary Lajos, Apr 02 2009] MAPLE with(combinat):T:=(n, i)->binomial(i, n)*binomial(10-i, 2-n): for n from 0 to 2 do seq(T(n, i), i=0+n..10-2+n) od; CROSSREFS Cf. A113899. Sequence in context: A037218 A070818 A285893 * A108909 A033365 A196093 Adjacent sequences:  A129533 A129534 A129535 * A129537 A129538 A129539 KEYWORD fini,nonn AUTHOR Zerinvary Lajos, May 29 2007 EXTENSIONS Edited by Charles R Greathouse IV, Oct 28 2009 STATUS approved

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Last modified January 19 18:31 EST 2020. Contains 331052 sequences. (Running on oeis4.)