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A091519 G.f.: sum(k>=0, 2^k*t*(1+t)/(1-t)^3, t=x^2^k). 2
1, 6, 9, 28, 25, 54, 49, 120, 81, 150, 121, 252, 169, 294, 225, 496, 289, 486, 361, 700, 441, 726, 529, 1080, 625, 1014, 729, 1372, 841, 1350, 961, 2016, 1089, 1734, 1225, 2268, 1369, 2166, 1521, 3000, 1681, 2646, 1849, 3388, 2025, 3174, 2209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..47.

FORMULA

a(n) = 2*n^2 - n*A000265(n) = n*A000265(n)*A038712(n).

Recurrence: a(0) = 0, a(2*n) = 2*a(n) + (2*n)^2, a(2*n+1) = (2*n+1)^2.

a((2*n-1)*2^p) = 2^p*(2^(p+1) - 1)*(2*n-1)^2, p >= 0. - Johannes W. Meijer, Jan 28 2013

MAPLE

nmax:=47: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := 2^p*(2^(p+1) - 1)*(2*n-1)^2 od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Jan 28 2013

PROG

(PARI) a(n)=2*n*n-n*n/2^valuation(n, 2)

(PARI) a(n)=if(n<1, 0, if(n%2==0, 2*a(n/2)+n^2, n^2))

CROSSREFS

Sequence in context: A007414 A274977 A025493 * A086491 A178597 A179908

Adjacent sequences:  A091516 A091517 A091518 * A091520 A091521 A091522

KEYWORD

nonn,mult,easy

AUTHOR

Ralf Stephan, Jan 18 2004

STATUS

approved

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Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)