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

%I A070878 #20 Jan 05 2025 19:51:37
%S A070878 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,
%T A070878 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,
%U A070878 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
%N A070878 Stern's diatomic array read by rows (version 2).
%C A070878 Row n has length 2^n + 1.
%H A070878 Harvey P. Dale, <a href="/A070878/b070878.txt">Table of n, a(n) for n = 0..10000</a>
%H A070878 C. Giuli and R. Giuli, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/17-2/giuli.pdf">A primer on Stern's diatomic sequence</a>, Fib. Quart., 17 (1979), 103-108, 246-248 and 318-320 (but beware errors).
%H A070878 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A070878 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.
%e A070878 Triangle begins:
%e A070878 1,0;
%e A070878 1,1,0;
%e A070878 1,2,1,1,0;
%e A070878 1,3,2,3,1,2,1,1,0;
%e A070878 ...
%t A070878 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 *)
%t A070878 Flatten[NestList[Riffle[#,Total/@Partition[#,2,1]]&,{1,0},6]] (* _Harvey P. Dale_, Dec 06 2014 *)
%Y A070878 Cf. A049456, A070879, A049455.
%Y A070878 Rows sums are A007051. See A293160 for number of distinct terms in each row.
%K A070878 nonn,tabf,nice,easy
%O A070878 0,7
%A A070878 _N. J. A. Sloane_, May 20 2002
%E A070878 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 07 2003