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.
Original entry on oeis.org
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
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)
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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
A049890
a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, 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 and a(3) = 2.
Original entry on oeis.org
1, 1, 2, 3, 6, 12, 24, 47, 93, 188, 376, 751, 1501, 2999, 5992, 11972, 23921, 47888, 95776, 191551, 383101, 766199, 1532392, 3064772, 6129521, 12258996, 24517897, 49035606, 98070837, 196140924, 392280350, 784557707, 1569109434
Offset: 1
Cf.
A049891 (similar, but with minus a(2*m)),
A049938 (similar, but with plus a(m)),
A049939 (similar, but with plus a(2*m)).
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lista(nn) = { nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 2; my(sa = vecsum(va)); for (n=4, nn, va[n] = sa - va[n - 1 - 2^logint(n-2,2)]; sa += va[n]; ); va; } \\ Petros Hadjicostas, Apr 27 2020
A049938
a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p 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.
Original entry on oeis.org
1, 1, 2, 5, 10, 20, 40, 81, 165, 326, 652, 1305, 2613, 5231, 10472, 20964, 41969, 83858, 167716, 335433, 670869, 1341743, 2683496, 5367012, 10734065, 21468214, 42936589, 85873504, 171747661, 343496630, 686995878, 1373996997, 2748004486, 5495988009, 10991976018, 21983952037, 43967904077
Offset: 1
From _Petros Hadjicostas_, Oct 01 2019: (Start)
a(4) = a(4 - 1 - 2^ceiling(-1 + log_2(3))) + a(1) + a(2) + a(3) = a(1) + a(1) + a(2) + a(3) = 5.
a(5) = a(5 - 1 - 2^ceiling(-1 + log_2(4))) + a(1) + a(2) + a(3) + a(4) = a(2) + a(1) + a(2) + a(3) + a(4) = 10.
a(6) = a(6 - 1 - 2^ceiling(-1 + log_2(5))) + a(1) + a(2) + a(3) + a(4) + a(5) = a(1) + a(1) + a(2) + a(3) + a(4) + a(5) = 20.
(End)
Cf.
A006257,
A049890 (similar, but with minus a(m)),
A049891 (similar, but with minus a(2*m)),
A049939 (similar, but with plus a(2*m)),
A049940,
A049960,
A049964,
A049978.
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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(n - 3/2 - 1/2*Bits:-Iff(n - 2, n - 2)); end proc; # Petros Hadjicostas, Oct 01 2019
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lista(nn) = { nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 2; my(sa = vecsum(va)); for (n=4, nn, va[n] = sa + va[n - 1 - 2^ceil(-1 + log(n-1)/log(2))]; sa += va[n]; ); va; } \\ Petros Hadjicostas, Apr 27 2020
Showing 1-3 of 3 results.