A070878 Stern's diatomic array read by rows (version 2).

1, 0, 1, 1, 0, 1, 2, 1, 1, 0, 1, 3, 2, 3, 1, 2, 1, 1, 0, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 0, 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, 0, 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

Offset

0,7

Comments

Row n has length 2^n + 1.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..10000

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

Each row is obtained by copying the previous row but interpolating the sums of pairs of adjacent terms. E.g. after 1 2 1 1 0 we get 1 1+2 2 2+1 1 1+1 1 1+0 0.

Example

Triangle begins:
1,0;
1,1,0;
1,2,1,1,0;
1,3,2,3,1,2,1,1,0;
...

Mathematica

row[1] = {1, 0}; row[n_] := row[n] = (r = row[n-1]; Riffle[r, Most[r + RotateLeft[r]]]); Flatten[ Table[row[n], {n, 1, 7}]] (* Jean-François Alcover, Nov 03 2011 *)
Flatten[NestList[Riffle[#, Total/@Partition[#, 2, 1]]&, {1, 0}, 6]] (* Harvey P. Dale, Dec 06 2014 *)

Crossrefs

Cf. A049456, A070879, A049455.

Rows sums are A007051. See A293160 for number of distinct terms in each row.

Sequence in context: A092921 A191607 A029387 * A228128 A060959 A342689

Adjacent sequences: A070875 A070876 A070877 * A070879 A070880 A070881

Keyword

nonn,tabf,nice,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