A128627 - OEIS

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A128627

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

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; refs; listen; history; internal format)

	OFFSET	`1,8`
	COMMENTS	`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 * A105422 A166291 A162986` `Adjacent sequences: A128624 A128625 A128626 * A128628 A128629 A128630`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Alford Arnold (Alford1940(AT)aol.com), Mar 22 2007`

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Last modified February 14 23:53 EST 2012. Contains 205689 sequences.