|
| |
|
|
A070878
|
|
Stern's diatomic array read by rows (version 2).
|
|
6
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
