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)).
-
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).
A049915
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), starting with a(1) = 1, a(2) = 2 and a(3) = 4.
Original entry on oeis.org
1, 2, 4, 5, 7, 17, 31, 50, 67, 182, 361, 710, 1387, 2642, 4756, 7580, 10222, 28022, 56041, 112070, 224107, 448082, 895636, 1789340, 3573742, 7127042, 14170036, 28004060, 54666862, 103996022, 187115026, 298238090, 402234112
Offset: 1
Cf.
A049914 (similar, but with minus a(m/2)),
A049962 (similar, but with plus a(m/2)),
A049963 (similar, but with plus a(m)).
-
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[2*n - 2 - 2^ceil(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).
Showing 1-3 of 3 results.