A134467 a(n) = n(n+1) - A000120(n), where A000120(n) = number of 1's in binary expansion of n.

0, 1, 5, 10, 19, 28, 40, 53, 71, 88, 108, 129, 154, 179, 207, 236, 271, 304, 340, 377, 418, 459, 503, 548, 598, 647, 699, 752, 809, 866, 926, 987, 1055, 1120, 1188, 1257, 1330, 1403, 1479, 1556, 1638, 1719, 1803, 1888, 1977, 2066, 2158, 2251, 2350, 2447, 2547

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

2^a(n) = denominator of [x^n] (1+x)^(1/2^n) for n>=0 (see A134098); similarily, 2^a(n) = denominator of [x^n] 1/(1-x)^(1/2^n) for n>=0 (see A134097).

Mathematica

Table[n(n+1)-DigitCount[n, 2, 1], {n, 0, 50}] (* Harvey P. Dale, Jul 13 2013 *)

Prog

(PARI) a(n)=n*(n+1) - subst(Pol(binary(n)), x, 1)
(Magma) [n^2 + Valuation(Factorial(n), 2): n in [0..60]]; // Vincenzo Librandi, Jun 12 2019

Crossrefs

Cf. A000120; A134097, A134098.

Sequence in context: A358306 A168567 A185440 * A178132 A227844 A191595

Adjacent sequences: A134464 A134465 A134466 * A134468 A134469 A134470

Keyword

nonn

Author

Paul D. Hanna, Oct 27 2007

Status

approved