A365396 Inverse permutation to A243571.

1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 13, 11, 14, 15, 21, 12, 16, 17, 22, 18, 23, 24, 34, 19, 25, 26, 35, 27, 36, 37, 55, 20, 28, 29, 38, 30, 39, 40, 56, 31, 41, 42, 57, 43, 58, 59, 89, 32, 44, 45, 60, 46, 61, 62, 90, 47, 63, 64, 91, 65, 92, 93, 144, 33, 48, 49, 66

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A000045(b(n) + 1) + Sum_{i=1..A000523(n)} binomial(i-1, b(n) - i) + Sum_{j=1..A000120(n) - 1} binomial(A133457(n, j), j) where b(n) = A056792(n).

Prog

(PARI) a(n) = my(L = logint(n, 2), wt = hammingweight(n), A = L + wt, m = 0); fibonacci(A+1) + sum(i=1, L, binomial(i-1, A-i)) + sum(j=0, L-1, if(bittest(n, j), m++; binomial(j, m)))

Crossrefs

Cf. A000045, A000120, A000523, A056792, A133457, A243571.

Sequence in context: A334436 A266195 A102530 * A345253 A358141 A266196

Adjacent sequences: A365393 A365394 A365395 * A365397 A365398 A365399

Keyword

nonn

Author

Alexander Khudyakov, Sep 03 2023

Status

approved