

A070879


Stern's diatomic array read by rows (version 3  same as version 2, A070878, but with final 0 in each row omitted).


6



1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 3, 1, 2, 1, 1, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 5, 4, 7, 3, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


COMMENTS

Row n has length 2^n.
From Yosu Yurramendi, Apr 08 2019: (Start)
The terms (n>0) may be written as a leftjustified array with rows of length 2^m:
1,
1, 1,
1, 2, 1, 1,
1, 3, 2, 3, 1, 2, 1, 1,
1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4,...
as well as rightjustified fashion:
1,
1, 1,
1, 2, 1, 1,
1, 3, 2, 3, 1, 2, 1, 1,
1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
... , 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
...
For properties see FORMULA section.
(End)


LINKS

Table of n, a(n) for n=0..100.
C. Giuli and R. Giuli, A primer on Stern's diatomic sequence, Fib. Quart., 17 (1979), 103108, 246248 and 318320 (but beware errors).
Index entries for sequences related to Stern's sequences


FORMULA

From Yosu Yurramendi, Apr 08 2019: (Start)
a(2^(m+1)+k1) = A002487(2^m+k); a(2^(m+1)+2^m+k1) = a(2^m+k1) for m >= 0, 0 <= k < 2^m.
a(2^(m+1)1(k+1)) = A002487(k+1); a(2^(m+1)+k)  a(2^m+k) = A002487(k) for m >= 0, 0 <= k < 2^m.
a(2^m1) = 1 for m >= 0; a(2^(m+1)+k1) = a(2^(m+1)k1) + a(2^m+k1) for m >= 0, 0 < k < 2^m.
a(2^m+2^m'+k'1) = a(2^(m'+1)+k'1)*(mm'1) + a(2^m'+k'1) for m >= 1, 0 <= m' < m, 0 <= k' < 2^m'.
(End)


CROSSREFS

Cf. A049456, A070878, A049455.
Rows sums are A007051.
Sequence in context: A344058 A134431 A211098 * A125644 A048821 A120221
Adjacent sequences: A070876 A070877 A070878 * A070880 A070881 A070882


KEYWORD

nonn,tabf,easy


AUTHOR

N. J. A. Sloane, May 20 2002


EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 07 2003


STATUS

approved



