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 A169969 Locations of row maxima in "crushed" version of Stern's diatomic array. 2
 1, 3, 5, 7, 11, 13, 21, 27, 43, 53, 85, 107, 171, 213, 341, 427, 683, 853, 1365, 1707, 2731, 3413, 5461, 6827, 10923, 13653, 21845, 27307, 43691, 54613, 87381, 109227, 174763, 218453, 349525, 436907, 699051, 873813, 1398101, 1747627, 2796203, 3495253 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Michel Marcus, Jan 22 2015: (Start) The Stern's diatomic array begins (see A049456). 1...............................1 1...............2...............1 1.......3.......2.......3.......1 1...4...3...5...2...5...3...4...1 1.5.4.7.3.8.5.7.2.7.5.8.3.7.4.5.1 ... The "crushed" version is obtained by removing the right column, and then squeezing everything to the left. 1; 1, 2; 1, 3, 2, 3; 1, 4, 3, 5, 2, 5, 3, 4; 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5; ... This gives sequence 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, ... (cf. A002487). The "crushed" array row maxima are: 1, 2, 3, 5, 8, ... (cf. A000045). The indices of these values in A002487 are 1, 3, 5, 7, 11, ... : this sequence. Note, for instance, that for 3rd row, the maximum which is 3, appears twice, at indices 5 and 7, giving 2 terms for this sequence. (End) LINKS S. Northshield, Stern's diatomic sequence 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, ..., Amer. Math. Monthly, 117 (2010), 581-598. FORMULA a(2n+1) + a(2n+2) = 3*2^(n+1), n>0 . - Yosu Yurramendi, Jun 29 2016 a(2n+3) = 3*2^(n+1) - a(n); a(2n+4) = 3*2^(n+1) + a(n), n>=0, a(0)=0 (new term), a(1)=1, a(2)=3 . - Yosu Yurramendi, Jun 29 2016 G.f.: x*(1 + 3*x + 4*x^2 + 4*x^3 + 4*x^4)/((1 + x^2)*(1 - 2*x^2)). - Ilya Gutkovskiy, Jun 29 2016 For n>1, a(n) = (2^(n/2 - 1)*(5 + 4*sqrt(2) + (-1)^n*(5 - 4*sqrt(2))) + cos(Pi*n/2) + sin(Pi*n/2))/3. - Vaclav Kotesovec, Jun 30 2016 a(2n) = a(2n-7) + 3*2^(n-1); a(2n-1) = a(2n-7) - 3*2^(n-1), n>=5 . - Yosu Yurramendi, Jul 06 2016 a(2n-1) = A168642(n), n>0; a(2n) = A048573(n), n>0; a(2n-1) = A026644(n) + 1, n>1; a(2n) = A084170(n) + 1, n>0 . - Yosu Yurramendi, Dec 11 2016 EXAMPLE G.f. = x + 3*x^2 + 5*x^3 + 7*x^4 + 11*x^5 + 13*x^6 + 21*x^7 + 27*x^8 + 43*x^9 + ... MATHEMATICA a[n_] := a[n] = If[n <= 5, {1, 3, 5, 7, 11}[[n]], a[n-2] + 2a[n-4]]; Array[a, 42] (* Jean-François Alcover, Dec 11 2016 *) PROG (PARI) fusc(n)=local(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); b; \\ from A002487 lista(nn) = {nb = 2^(nn+1)-1; vall = vector(nb, n, fusc(n)); for (n=1, nn, vmax = 0; for (j=2^(n-1), 2^n-1, if (vall[j] > vmax, vmax = vall[j]); ); for (j=2^(n-1), 2^n-1, if (vall[j] == vmax, print1(j, ", ")); ); ); } \\ Michel Marcus, Jan 22 2015 CROSSREFS Sequence in context: A249077 A126960 A119753 * A174350 A240476 A040140 Adjacent sequences:  A169966 A169967 A169968 * A169970 A169971 A169972 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Aug 08 2010 EXTENSIONS More terms from Michel Marcus, Jan 22 2015 STATUS approved

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