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 A049942 a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 3, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1. 4
 1, 1, 3, 6, 12, 24, 48, 98, 199, 393, 786, 1574, 3151, 6308, 12628, 25280, 50610, 101123, 202246, 404494, 808991, 1617988, 3235988, 6472000, 12944050, 25888201, 51776596, 103553585, 207107958, 414217493, 828438143, 1656882606, 3313777864, 6627530449, 13255060898, 26510121798, 53020243599 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Petros Hadjicostas, Table of n, a(n) for n = 1..3323 FORMULA From Petros Hadjicostas, Oct 25 2019: (Start) a(n) = a(n - 1 - 2^ceiling(-1 + log_2(n-1))) + Sum_{i = 1..n-1} a(i) for n >= 3. a(n) = a((1 + A006257(n-2))/2) + Sum_{i = 1..n-1} a(i) for n >= 3. (End) EXAMPLE From Petros Hadjicostas, Oct 25 2019: (Start) a(3) = a(3 - 1 - 2^ceiling(-1 + log_2(3-1))) + a(1) + a(2) = a(1) + a(1) + a(2) = 3. a(4) = a(4 - 1 - 2^ceiling(-1 + log_2(4-1))) + a(1) + a(2) + a(3) = a(1) + a(1) + a(2) + a(3) = 6. a(5) = a(5 - 1 - 2^ceiling(-1 + log_2(5-1))) + a(1) + a(2) + a(3) + a(4) = a(2) + a(1) + a(2) + a(3) + a(4) = 12. a(6) = a(6 - 1 - 2^ceiling(-1 + log_2(6-1))) + a(1) + a(2) + a(3) + a(4) + a(5) = a(1) + a(1) + a(2) + a(3) + a(4) + a(5) = 24. (End) MAPLE s := proc(n) option remember; `if`(n<1, 0, a(n)+s(n-1)) end: a := proc(n) option remember; `if`(n<3, 1, s(n-1)+        a(n-3/2-1/2*Bits:-Iff(n-2, n-2)))      end: seq(a(n), n=1..50);  # Petros Hadjicostas, Oct 25 2019 CROSSREFS Cf. A006257, A049894 (similar with minus a(m)), A049895 (similar with minus a(2*m)), A049943 (similar with plus a(2*m)). Sequence in context: A170684 A003945 A007283 * A200463 A099844 A165929 Adjacent sequences:  A049939 A049940 A049941 * A049943 A049944 A049945 KEYWORD nonn AUTHOR EXTENSIONS More terms from Petros Hadjicostas, Oct 25 2019 STATUS approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)