A363417 a(n) = Sum_{j=0..2^n - 1} b(j) for n >= 0 where b(n) = (A023416(n) + 1)*b(A053645(n)) + [A036987(n) = 0]*b(A266341(n)) for n > 0 with b(0) = 1.

1, 2, 6, 23, 106, 566, 3415, 22872, 167796, 1334596, 11414192, 104270906, 1011793389, 10379989930, 112134625986, 1271209859403, 15077083642150, 186588381229340, 2403775013224000, 32168379148440968, 446341838086450308, 6410107231501731012, 95136428354649665256

Offset

0,2

Comments

Note that [A036987(n) = 0]*b(A266341(n)) is the same as max((1 - T(n, j))*b(A053645(n) + 2^j*(1 - T(n, j))) | 0 <= j <= A000523(n)) where T(n, k) = floor(n/2^k) mod 2.

In fact b(n) is a generalization of A347205 just as A329369 is a generalization of A341392.

Links

Table of n, a(n) for n=0..22.

Prog

(PARI) A063250(n)=my(L=logint(n, 2), A=0); for(i=0, L, my(B=n\2^(L-i)+1); A++; A-=logint(B, 2)==valuation(B, 2)); A
upto(n)=my(v, v1); v=vector(2^n, i, 0); v[1]=1; v1=vector(n+1, i, 0); v1[1]=1; for(i=1, #v-1, my(L=logint(i, 2), A=i - 2^L, B=A063250(i)); v[i+1]=(L - hammingweight(i) + 2)*v[A+1] + if(B>0, v[A + 2^(B-1) + 1])); for(i=1, n, v1[i+1]=v1[i] + sum(j=2^(i-1)+1, 2^i, v[j])); v1

Crossrefs

Cf. A000523, A023416, A036987, A053645, A266341.

Similar recurrences: A284005, A329369, A341392, A347205.

Sequence in context: A288912 A193321 A263780 * A125273 A336070 A187761

Adjacent sequences: A363414 A363415 A363416 * A363418 A363419 A363420

Keyword

nonn,changed

Author

Mikhail Kurkov, Jun 11 2023 [verification needed]

Status

approved