login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178568 Triangle read by rows, antidiagonals of an array generated from a(2n) = r*a(n), a(2n+1) = a(n) + a(n+1). 6
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) = r*a(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 + r*x + x^2).

Let q(x) = (1 + r*x + 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: A267409 A104469 A144112 * A104660 A212125 A282936

Adjacent sequences:  A178565 A178566 A178567 * A178569 A178570 A178571

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, May 29 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 19:26 EST 2018. Contains 299422 sequences. (Running on oeis4.)