A163095 - OEIS

A163095

a(n) = A000788(n)^2.

0, 1, 4, 16, 25, 49, 81, 144, 169, 225, 289, 400, 484, 625, 784, 1024, 1089, 1225, 1369, 1600, 1764, 2025, 2304, 2704, 2916, 3249, 3600, 4096, 4489, 5041, 5625, 6400, 6561, 6889, 7225, 7744, 8100, 8649, 9216, 10000, 10404, 11025, 11664, 12544, 13225

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..44.

Hsien-Kuei Hwang, S. Janson, T.-H. Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint 2016.

Hsien-Kuei Hwang, S. Janson, T.-H. Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585.

MAPLE

read("transforms") : A000788 := proc(n) add( wt(j), j=0..n) ; end: A163095 := proc(n) A000788(n)^2 ; end: seq(A163095(n), n=0..100) ; # R. J. Mathar, Feb 22 2010

MATHEMATICA

Accumulate@ DigitCount[Range[0, 44], 2, 1]^2 (* Michael De Vlieger, Jan 23 2019 *)

PROG

(Python)

def A163095(n): return sum(i.bit_count() for i in range(1, n+1))**2 # Chai Wah Wu, Mar 02 2023

CROSSREFS

Cf. A000788.

Sequence in context: A235001 A087055 A135556 * A075576 A353295 A363428

Adjacent sequences: A163092 A163093 A163094 * A163096 A163097 A163098

KEYWORD

easy,nonn,base

AUTHOR

Omar E. Pol, Aug 06 2009

EXTENSIONS

Extended by R. J. Mathar, Feb 22 2010

STATUS

approved

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