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

Author

N. J. A. Sloane, May 20 2002

Keywords

• nonn
• tabf
• easy

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

• 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

Crossrefs

Cf. A049456, A070878, A049455.

Rows sums are A007051.

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)

Extensions

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