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 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). 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 A077042 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

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)