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A197354
a(n) = Sum_{k>=0} A030308(n,k)*(2k+1).
3
0, 1, 3, 4, 5, 6, 8, 9, 7, 8, 10, 11, 12, 13, 15, 16, 9, 10, 12, 13, 14, 15, 17, 18, 16, 17, 19, 20, 21, 22, 24, 25, 11, 12, 14, 15, 16, 17, 19, 20, 18, 19, 21, 22, 23, 24, 26, 27, 20, 21, 23, 24, 25, 26, 28, 29, 27, 28, 30, 31, 32, 33, 35, 36, 13, 14, 16
OFFSET
0,3
COMMENTS
For any k >= 0, A000700(k) equals the number of occurrences of k in the sequence. - Rémy Sigrist, Jan 19 2019
LINKS
FORMULA
a(2^n-1) = n^2.
a(n) mod 2 = A010060(n).
G.f.: (1/(1 - x))*Sum_{k>=0} (2*k + 1)*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jul 23 2017
PROG
(PARI) a(n) = my (b=Vecrev(binary(n))); sum(i=1, #b, if (b[i], 2*i-1, 0)) \\ Rémy Sigrist, Jan 19 2019
CROSSREFS
Other sequences that are built by replacing 2^k in the binary representation with other numbers: A022290 (Fibonacci), A029931 (natural numbers), A059590 (factorials), A089625 (primes).
Sequence in context: A352025 A112768 A298420 * A089399 A003619 A377721
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Oct 14 2011
STATUS
approved