A049914
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) = 1, a(2) = 2 and a(3) = 4.
Original entry on oeis.org
1, 2, 4, 6, 11, 23, 45, 88, 174, 353, 705, 1408, 2814, 5623, 11234, 22446, 44849, 89785, 179569, 359136, 718270, 1436535, 2873058, 5746094, 11492145, 22984204, 45968229, 91936106, 183871509, 367741612, 735480415, 1470955219
Offset: 1
Cf.
A049915 (similar, but with minus a(2*m)),
A049962 (similar, but with plus a(m)),
A049963 (similar, but with plus a(2*m)).
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lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 2; va[3] = 4; 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 26 2020 (with nn > 2).
A049962
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) = 1, a(2) = 2, and a(3) = 4.
Original entry on oeis.org
1, 2, 4, 8, 17, 33, 67, 136, 276, 545, 1091, 2184, 4372, 8753, 17522, 35078, 70225, 140315, 280631, 561264, 1122532, 2245073, 4490162, 8980358, 17960785, 35921710, 71843689, 143687924, 287376941, 574756070, 1149516521, 2299041811
Offset: 1
Cf.
A049914 (similar, but with minus a(m)),
A049915 (similar, but with minus a(2*m)),
A049963 (similar, but with plus a(2*m)).
-
s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)); end proc;
a := proc(n) option remember; `if`(n < 4, [1, 2, 4][n], s(n - 1) + a(-2^ceil(log[2](n - 1) - 1) + n - 1)); end proc;
seq(a(n), n = 1 .. 40); # Petros Hadjicostas, Apr 23 2020
-
lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 2; va[3] = 4; 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 26 2020 (with nn > 2).
A049963
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) = 1, a(2) = 2 and a(3) = 4.
Original entry on oeis.org
1, 2, 4, 9, 25, 43, 93, 220, 617, 1016, 2039, 4112, 8401, 17598, 38292, 90070, 252612, 415156, 830319, 1660672, 3321521, 6643838, 13290772, 26595030, 53262532, 106850150, 214945816, 434874798, 889700788, 1859656696
Offset: 1
From _Petros Hadjicostas_, Sep 25 2019: (Start)
a(4) = a(1 + A006257(4-2)) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 9.
a(7) = a(1 + A006257(7-2)) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6) = a(4) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6) = 93.
(End)
Cf.
A049914 (similar, but with minus a(m/2)),
A049915 (similar, but with minus a(m)),
A049962 (similar, but with plus a(m/2)).
-
a := proc(n) local i; option remember; if n < 4 then return [1, 2, 4][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..40); # Petros Hadjicostas, Sep 25 2019, courtesy of Peter Luschny
Showing 1-3 of 3 results.
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