id:A128627 - OEIS Search Results

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Triangular array illustrating the application of cyclic partitions to the computation of partitions of an integer into parts of k kinds. (cf A060850).

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1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 2, 2, 3, 0, 1, 2, 5, 3, 4, 0, 1, 4, 6, 9, 4, 5, 0, 1, 4, 13, 12, 14, 5, 6, 0, 1, 7, 16, 28, 20, 20, 6, 7, 0, 1 (list; table; graph; listen)

	OFFSET	`1,8`
	COMMENT	`The array is constructed by summing sequences associated with each cyclic partition as indicated below: (n' here denotes the sum of preceding sequences).` `4.......1......2......3......................................` `22......1......3......6......................................` `4'......2......5......9......................................` `5.......1......2......3......4...............................` `32......1......4......9......16..............................` `5'......2......6......12......20.............................` `6.......1......2......3.......4.......5.......6.......7.......8......9` `42......1......4......9......16......25......36......49......64......81` `33......1......3......6......10......15......21......28......36......45` `222.....1......4......10......20......35......56......84......120...165` `6'......4......13.....28......50......80....119......168......228...300` `7.......1......2......3.......4.......5.......6.......7.......8.......9` `52......1......4......9......16......25......36......49......64......81` `43......1......4......9......16......25......36......49......64......81` `322.....1......6......18......40.....75.....126......196.....288.....405` `7'......4......16.....39......76......130...204......301.....424.....576` `8.......1......2......3.......4.......5.......6.......7.......8.......9` `62......1......4......9......16......25......36......49......64......81` `53......1......4......9......16......25......36......49......64......81` `44......1......3......6......10......15......21......28......36......45` `422.....1......6......18......40......75......126......196......288......405` `332.....1......6......18......40......75......126......196......288......405` `2222....1......5......15......35......70......126......210......330......495` `8'......7......30.....78......161......290......477......735......1078......1521`
	EXAMPLE	`The diagonal 9th diagonal of A060850 is 22 185 810 2580 6765 ... and can be computed from a(n) and A007318 as illustrated:` `1..................` `0......1............` `1......0......1......` `1......2......0......1` `2......2......3......0` `2......5......3......4` `4......6......9......4` `4......13....12......14` `7......16....28......20` `.......30....39......50` `.............78......76` `....................161` `times` `1..................` `1......9............` `1......8......45......` `1......7......36......165` `1......6......28......120` `1......5......21......84` `1......4......15......56` `1......3......10......35` `1......2......6......20` `.......1......3......10` `..............1......4` `.....................1` `yields` `1..................` `0......9............` `1......0......45......` `1......14......0.......165` `2......12......84......0` `2......25......63......336` `4......24......135.....224` `4......39......120.....490` `7......32......168.....400` `.......30......117.....500` `...............78......304` `.......................161` `summing to` `22.....185.....810.....2580 ...`
	CROSSREFS	`Cf. A060850 A007318 A002865.` `Sequence in context: A033773 A029275 A058739 this_sequence A105422 A128584 A080099` `Adjacent sequences: A128624 A128625 A128626 this_sequence A128628 A128629 A128630`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Alford Arnold (Alford1940(AT)aol.com), Mar 22 2007`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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