[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A049939
a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = 2*n - 2 - 2^(p+1) and p is the unique integer such that 2^p < n-1 <= 2^(p+1), with a(1) = a(2) = 1 and a(3) = 2.
10
1, 1, 2, 5, 14, 24, 52, 123, 345, 568, 1140, 2299, 4697, 9839, 21409, 50358, 141235, 232113, 464230, 928479, 1857057, 3714559, 7430849, 14869238, 29778995, 59739745, 120175856, 243137792, 497430263, 1039731033, 2262860113
OFFSET
1,3
FORMULA
a(n) = a(1 + A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4 with a(1) = a(2) = 1 and a(3) = 2.
EXAMPLE
From Petros Hadjicostas, Sep 24 2019: (Start)
a(4) = a(1 + A006257(4-2)) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 1 + 1 + 1 + 2 = 5.
a(5) = a(1 + A006257(5-2)) + a(1) + a(2) + a(3) + a(4) = a(4) + a(1) + a(2) + a(3) + a(4) = 5 + 1 + 1 + 2 + 5 = 14.
a(6) = a(1 + A006257(6-2)) + a(1) + a(2) + a(3) + a(4) + a(5) = a(2) + a(1) + a(2) + a(3) + a(4) + a(5) = 1 + 1 + 1 + 2 + 5 + 14 = 24.
(End)
MAPLE
a := proc(n) local i; option remember; if n < 4 then return [1, 1, 2][n]; end if; add(a(i), i = 1 .. n - 1) + a(2*n - 3 - Bits:-Iff(n - 2, n - 2)); end proc;
seq(a(n), n = 1 .. 37); # Petros Hadjicostas, Sep 24 2019, courtesy of Peter Luschny
CROSSREFS
Cf. A006257, A049890 (similar, but with minus a(m/2)), A049891 (similar, but with minus a(m)), A049938 (similar, but with plus a(m/2)), A049940, A049960, A049964.
Sequence in context: A321287 A076664 A220477 * A296302 A240401 A133375
KEYWORD
nonn
EXTENSIONS
Name edited by Petros Hadjicostas, Sep 24 2019
STATUS
approved