A165196 - OEIS

%I #8 Sep 25 2025 00:02:22

%S 1,2,4,5,7,12,14,15,17,22,37,42,44,49,51,52,54,59,74,79,94,146,161,

%T 166,168,173,188,193,195,200,202,203,205,210,225,230,245,297,312,317,

%U 332,384,587,639,654,706,721,726,728,733,748,753,768,820,835,840,842,847,862,867,869,874,876,877

%N Partial sums of A165195.

%H Andrew Howroyd, <a href="/A165196/b165196.txt">Table of n, a(n) for n = 1..4096</a>

%F Partial sums of A165195.

%F a(2^n) = A000110(n-1).

%e a(8) = 15 = sum of the first 8 terms of A165195: (1, 1, 2, 1, 2, 5, 2, 1...).

%o (PARI) seq(n)={my(v=vector(n,i,i--;hammingweight(bitxor(i, i>>1))), b=Vec(serlaplace(exp(exp(x+O(x*x^vecmax(v))) - 1)))); v=vector(#v, i, b[1+v[i]]); for(i=2, #v, v[i]+=v[i-1]); v} \\ _Andrew Howroyd_, Sep 24 2025

%Y Cf. A000110, A165194, A165195.

%K nonn

%O 1,2

%A _Gary W. Adamson_, Sep 06 2009

%E a(25) corrected and a(33) onwards from _Andrew Howroyd_, Sep 24 2025