A379818 a(2n+1) = a(n) for n >= 0, a(2n) = a(n) + a(n - 2^f(n)) + a(2n - 2^f(n)) + a(A025480(n-1)) for n > 0 with a(0) = 1 where f(n) = A007814(n).

1, 1, 4, 1, 10, 4, 10, 1, 22, 10, 28, 4, 49, 10, 22, 1, 46, 22, 64, 10, 118, 28, 64, 4, 190, 49, 118, 10, 190, 22, 46, 1, 94, 46, 136, 22, 256, 64, 148, 10, 424, 118, 292, 28, 478, 64, 136, 4, 661, 190, 478, 49, 796, 118, 256, 10, 1177, 190, 424, 22, 661, 46

Offset

0,3

Links

Table of n, a(n) for n=0..61.

Formula

Conjecture: a(2^m*(2k+1)) = Sum_{j=0..m} (binomial(m+2, j+1) - binomial(m, j))*a(2^j*k) for m >= 0, k >= 0 with a(0) = 1.

Prog

(PARI) list(n) = my(A, v = vector(n+1, i, 0)); v[1] = 1; for(i=1, n, v[i+1] = v[i\2+1] + if(i%2, 0, A = 1 << valuation(i/2, 2); v[i/2-A+1] + v[i-A+1] + v[i\(4*A)+1])); v

Crossrefs

Cf. A007814, A025480, A329369, A341392, A347205.

Sequence in context: A334161 A039806 A030320 * A104713 A185945 A186368

Adjacent sequences: A379815 A379816 A379817 * A379819 A379820 A379821

Keyword

nonn,base

Author

Mikhail Kurkov, Jan 03 2025

Status

approved