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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 left-justified 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 right-justified 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), 103-108, 246-248 and 318-320 (but beware errors).

Index entries for sequences related to Stern's sequences

FORMULA

From Yosu Yurramendi, Apr 08 2019: (Start)

a(2^(m+1)+k-1) = A002487(2^m+k); a(2^(m+1)+2^m+k-1) = a(2^m+k-1)  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^m-1) = 1 for m >= 0; a(2^(m+1)+k-1) = a(2^(m+1)-k-1) + a(2^m+k-1) for m >= 0, 0 < k < 2^m.

a(2^m+2^m'+k'-1) = a(2^(m'+1)+k'-1)*(m-m'-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

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Last modified December 1 13:22 EST 2021. Contains 349429 sequences. (Running on oeis4.)