A350311 Replace 2^k in the binary expansion of n with A000930(k+2), Narayana's cows sequence.

0, 1, 2, 3, 3, 4, 5, 6, 4, 5, 6, 7, 7, 8, 9, 10, 6, 7, 8, 9, 9, 10, 11, 12, 10, 11, 12, 13, 13, 14, 15, 16, 9, 10, 11, 12, 12, 13, 14, 15, 13, 14, 15, 16, 16, 17, 18, 19, 15, 16, 17, 18, 18, 19, 20, 21, 19, 20, 21, 22, 22, 23, 24, 25, 13, 14, 15, 16, 16, 17

Offset

0,3

Comments

A048715(n) = m, if and only if a(n) = m and for all k > n a(k) > m.

Links

Table of n, a(n) for n=0..69.

Maple

b:= (n, i, j, k)->`if`(n=0, 0, k*irem(n, 2, 'q')+b(q, j, k, i+k)):
a:= n-> b(n, 1$3):
seq(a(n), n=0..100);  # Alois P. Heinz, Jan 26 2022

Prog

(Python)
def Interpretation(n):
    f0, f1, f2, r = 1, 1, 1, 0
    while n > 0:
        if n%2 == 1:
            r = r+f0
        n, f0, f1, f2 = n//2, f0+f2, f0, f1
    return r
n = 0
while n <= 69:
    print(Interpretation(n), end = ", ")
    n += 1
(PARI) my(p=Mod('x, 'x^3-'x^2-1)); a(n) = vecsum(Vec(lift(subst(Pol(binary(n))*'x^2, 'x, p)))); \\ Kevin Ryde, Dec 26 2021

Crossrefs

Cf. A000930, A048715, A350215, A350312.

Cf. A022290 (analog for Fibonacci numbers).

Sequence in context: A202704 A273004 A029931 * A331297 A322806 A332809

Adjacent sequences: A350308 A350309 A350310 * A350312 A350313 A350314

Keyword

nonn,base

Author

A.H.M. Smeets, Dec 24 2021

Status

approved