cp's OEIS Frontend

A070879 Stern's diatomic array read by rows (version 3 - same as version 2, A070878, but with final 0 in each row omitted).

%I A070879 #23 Jan 05 2025 19:51:37
%S A070879 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,
%T A070879 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,
%U A070879 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
%N A070879 Stern's diatomic array read by rows (version 3 - same as version 2, A070878, but with final 0 in each row omitted).
%C A070879 Row n has length 2^n.
%C A070879 From _Yosu Yurramendi_, Apr 08 2019: (Start)
%C A070879 The terms (n>0) may be written as a left-justified array with rows of length 2^m:
%C A070879 1,
%C A070879 1, 1,
%C A070879 1, 2, 1, 1,
%C A070879 1, 3, 2, 3, 1, 2, 1, 1,
%C A070879 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
%C A070879 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4,...
%C A070879 as well as right-justified fashion:
%C A070879                                                                                 1,
%C A070879                                                                              1, 1,
%C A070879                                                                        1, 2, 1, 1,
%C A070879                                                            1, 3, 2, 3, 1, 2, 1, 1,
%C A070879                                    1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
%C A070879      ... , 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
%C A070879 ...
%C A070879 For properties see FORMULA section.
%C A070879 (End)
%H A070879 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 A070879 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A070879 From _Yosu Yurramendi_, Apr 08 2019: (Start)
%F A070879 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.
%F A070879 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.
%F A070879 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.
%F A070879 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'.
%F A070879 (End)
%Y A070879 Cf. A049456, A070878, A049455.
%Y A070879 Rows sums are A007051.
%K A070879 nonn,tabf,easy
%O A070879 0,5
%A A070879 _N. J. A. Sloane_, May 20 2002
%E A070879 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 07 2003