A070879 Stern's diatomic array read by rows (version 3 - same as version 2, A070878, but with final 0 in each row omitted).

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

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