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A000773 Number of numbers == 0 (mod 3) in range 2^n to 2^(n+1) with odd number of 1's in binary expansion. 3
0, 0, 0, 1, 1, 6, 8, 29, 45, 130, 220, 561, 1001, 2366, 4368, 9829, 18565, 40410, 77540, 164921, 320001, 669526, 1309528, 2707629, 5326685, 10919090, 21572460, 43942081, 87087001, 176565486, 350739488, 708653429, 1410132405, 2841788170, 5662052980 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

The first numbers with this property are 21, 42, 69, 81, 84, 87, 93,  and 117. - T. D. Noe, Jun 20 2012

LINKS

T. D. Noe, Table of n, a(n) for n = 1..501

Nina Chen, Recurrence relation.

Index entries for linear recurrences with constant coefficients, signature (1,5,-3,-6).

FORMULA

a(n) = (1/6)*(2^n - (-1)^n - 3^((n+1)/2)). G.f.: x^3 / ((1+x)*(1-2*x)*(1-3*x^2)). - Ralf Stephan, Aug 08 2004

a(n) = a(n-1) + 2 * a(n-2) + 3^(n/2) * (1 + (-1)^n) / 18 for all n in Z. - Michael Somos, Jan 23 2014

a(n) = - 6 * a(n-4) - 3 * a(n-3) + 5 * a(n-2) + a(n-1) for n > 4. - Hugo Pfoertner, Jun 13 2017

EXAMPLE

G.f. = x^4 + x^5 + 6*x^6 + 8*x^7 + 29*x^8 + 45*x^9 + 130*x^10 + 220*x^11 + ...

MATHEMATICA

nn = 35; CoefficientList[Series[x^3/((1 + x) (1 - 2 x) (1 - 3 x^2)), {x, 0, nn}], x] (* T. D. Noe, Jun 20 2012 *)

CROSSREFS

Cf. A000069.

Sequence in context: A237290 A229335 A007829 * A258283 A039720 A056097

Adjacent sequences:  A000770 A000771 A000772 * A000774 A000775 A000776

KEYWORD

easy,nonn

AUTHOR

Russ Cox

STATUS

approved

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Last modified November 14 18:55 EST 2018. Contains 317214 sequences. (Running on oeis4.)