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

Author

N. J. A. Sloane, May 20 2002

Keywords

• nonn
• tabf
• nice
• easy

Comments

Row n has length 2^n + 1.

Examples

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

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

Crossrefs

Cf. A049456, A070879, A049455.

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

Programs

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 *)

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.

Extensions

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