A049922
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) = 3 and a(3) = 2.
Original entry on oeis.org
1, 3, 2, 5, 8, 18, 34, 69, 135, 274, 546, 1093, 2183, 4363, 8716, 17416, 34797, 69662, 139322, 278645, 557287, 1114571, 2229132, 4458248, 8916461, 17832856, 35665573, 71330874, 142661201, 285321312, 570640444, 1141276535, 2282544370
Offset: 1
Cf.
A049923 (similar, but with minus a(2*m)),
A049970 (similar, but with plus a(m)),
A049971 (similar, but with plus a(2*m)).
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lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 3; 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 26 2020 (with nn > 2)
A049923
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) = 3, and a(3) = 2.
Original entry on oeis.org
1, 3, 2, 3, 6, 12, 24, 39, 51, 138, 276, 543, 1059, 2019, 3633, 5790, 7809, 21405, 42810, 85611, 171195, 342291, 684177, 1366878, 2729985, 5444355, 10824504, 21392328, 41760069, 79442661, 142937349, 227824365, 307267026, 842358414
Offset: 1
Cf.
A049922 (similar, but with minus a(m/2)),
A049970 (similar, but with plus a(m/2)),
A049971 (similar, but with plus a(m)).
-
lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 3; va[3] = 2; 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)
A049970
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) = 3, and a(3) = 2.
Original entry on oeis.org
1, 3, 2, 7, 16, 30, 62, 123, 251, 496, 994, 1987, 3979, 7967, 15948, 31928, 63917, 127712, 255426, 510851, 1021707, 2043423, 4086860, 8173752, 16347565, 32695258, 65390761, 130782020, 261565033, 523132058, 1046268104, 2092544189
Offset: 1
Cf.
A049922 (similar, but with minus a(m)),
A049923 (similar, but with minus a(2*m)),
A049971 (similar, but with plus a(2*m)).
-
a[1] = 1; a[2] = 3; a[3] = 2; a[n_] := a[n] = Sum[a[k], {k, 1, n - 1}] + a[n - 1 - 2^Floor[Log[2, n - 2]]]; Table[a[n], {n, 1, 32}] (* Vaclav Kotesovec, Apr 26 2020 *)
-
lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 3; 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 26 2020 (with nn > 2)
Showing 1-3 of 3 results.