A049893 a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = 2^(p+1) + 2 - n 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) = 3.

1, 1, 3, 4, 8, 13, 27, 56, 112, 169, 367, 748, 1501, 3006, 6013, 12028, 24056, 36085, 78185, 159377, 320259, 641271, 1282923, 2566044, 5132145, 10264346, 20528721, 41057456, 82114917, 164229838, 328459677, 656919356, 1313838712, 1970758069, 4269975817, 8704181473

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3326
• Frankie Mennicucci, On the Number of Strong Dominating Sets in a Graph, Master's Thesis, Montclair State Univ. (2024). See p. 17.

Crossrefs

Cf. A049885.

Programs

Maple

s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:
a := proc(n) option remember;
`if`(n < 4, [1,1,3][n], s(n - 1) - a(2^ceil(log[2](n - 1)) + 2 - n)):
end proc:
seq(a(n), n = 1..34); # Petros Hadjicostas, Nov 11 2019

Mathematica

nn = 36; a[1] = a[2] = 1; a[3] = 3; s = 5; Do[Set[k, s - a[2^(Ceiling@ Log2[n - 1]) + 2 - n]]; a[n] = k; s += k, {n, 4, nn}]; Array[a, nn] (* Michael De Vlieger, Oct 21 2024 *)

Extensions

Name edited by Petros Hadjicostas, Nov 11 2019

More terms from Michael De Vlieger, Oct 21 2024