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 A070879 Stern's diatomic array read by rows (version 3 - same as version 2, A070878, but with final 0 in each row omitted). 6
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row n has length 2^n. From Yosu Yurramendi, Apr 08 2019: (Start) The terms (n>0) may be written as a left-justified array with rows of length 2^m: 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, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4,... as well as right-justified fashion:                                                                                 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,      ... , 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, ... For properties see FORMULA section. (End) LINKS 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). FORMULA From Yosu Yurramendi, Apr 08 2019: (Start) 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. 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. 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. 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'. (End) CROSSREFS Cf. A049456, A070878, A049455. Rows sums are A007051. Sequence in context: A344058 A134431 A211098 * A125644 A048821 A120221 Adjacent sequences:  A070876 A070877 A070878 * A070880 A070881 A070882 KEYWORD nonn,tabf,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

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Last modified December 1 13:22 EST 2021. Contains 349429 sequences. (Running on oeis4.)