A178568 - OEIS

This site is supported by donations to The OEIS Foundation.

A178568

Triangle read by rows, antidiagonals of an array generated from a(2n) = r*a(n), a(2n+1) = a(n) + a(n+1).

1, 1, 1, 1, 2, 2, 1, 3, 3, 1, 1, 4, 4, 4, 3, 1, 5, 5, 9, 5, 2, 1, 6, 6, 16, 7, 6, 3, 1, 7, 7, 25, 9, 12, 7, 1, 1, 8, 8, 36, 11, 20, 13, 8, 4, 1, 9, 9, 49, 13, 30, 21, 27, 9, 3, 1, 10, 10, 64, 15, 42, 31, 64, 16, 10, 5, 1, 11, 11, 81, 17, 56, 43, 125, 25, 21, 11, 2 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`1,5`
	COMMENTS	`Companion to A178239 (the latter generated from a(n) = a(2n), a(2n+1) = ra(n) + a(n+1).` `Row sums = A169826: (1, 2, 5, 8, 16, 27, 45, 69, 109,...).` `Polcoeff row r of the array as f(x) satisfies f(x)/f(x^2) = (1 + rx + x^2).` `Let q(x) = (1 + rx + x^2). Then polcoeff row r = q(x) q(x^2) * q(x^4) * q(x^8) * ...` `Right border of the triangle = A002487: (1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5,...).` `Terms in r-th row mod r (for r>1) = (1, 0, 1, 0, 1, 0,...).`
	LINKS	`Table of n, a(n) for n=1..78.`
	FORMULA	`a(2n) = r*a(n), a(2n+1) = a(n) + a(n+1)` `Given (1, r, 1, 0, 0, 0,...) in each column of an infinite lower triangular` `matrix M; shifted down twice from the previous column. r-th row of the array` `= Lim_{n->inf} M^n.`
	EXAMPLE	`First few rows of the array =` `1,...1,...2,...1,...3,...2,...3,...1,...4,...3,...5,...2,...5,...3,...` `1,...2,...3,...4,...5,...6,...7,...8,...9,..10,..11,..12,..13,..14,...` `1,...3,...4,...9,...7,..12,..13,..27,..16,..21,..19,..36,..25,..39,...` `1,...4,...5,..16,...9,..20,..21,..64,..25,..36,..29,..80,..41,..84,...` `1,...5,...6,..25,..11,..30,..31,.125,..36,..55,..41,.150,..61,.155,...` `1,...6,...7,..36,..13,..42,..43,.216,..49,..78,..55,.252,..85,.258,...` `1,...7,...8,..49,..15,..56,..57,.343,..64,.105,..71,.392,.113,.399,...` `1,...8,...9,..64,..17,..72,..73, 512,..81,.136,..89,.576,.145,.584,...` `...` `First few rows of the triangle =` `1;` `1, 1;` `1, 2, 2;` `1, 3, 3, 1;` `1, 4, 4, 4, 3;` `1, 5, 5, 9, 5, 2;` `1, 6, 6, 16, 7, 6, 3;` `1, 7, 7, 25, 9, 12, 7, 1;` `1, 8, 8, 36, 11, 20, 13, 8, 4;` `1, 9, 9, 49, 13, 30, 21, 27, 9, 3;` `1, 10, 10, 64, 15, 42, 31, 64, 16, 10, 5;` `1, 11, 11, 81, 17, 56, 43, 125, 25, 21, 11, 2;` `1, 12, 12, 100, 19, 72, 57, 216, 36, 36, 19, 12, 5;` `1, 13, 13, 121, 21, 90, 73, 343, 49, 55, 29, 36, 13, 3;` `1, 14, 14, 144, 23, 110, 91, 512, 64, 78, 41, 80, 25, 14, 4;` `...`
	CROSSREFS	`Cf. A002487, A178239` `Sequence in context: A103360 A104469 A144112 * A104660 A212125 A220073` `Adjacent sequences: A178565 A178566 A178567 * A178569 A178570 A178571`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Gary W. Adamson, May 29 2010`
	STATUS	`approved`

Content is available under The OEIS End-User License Agreement .

Last modified May 23 12:14 EDT 2013. Contains 225587 sequences.