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 A178804 When dealing cards into 3 piles (Left, Center, Right), the number of cards in the n-th card's pile, if dealing in a pattern L, C, R, C, L, C, R, C, L, C, ... [as any thoughtful six-year-old will try to do when sharing a pile of candy among 3 people]. 3

%I

%S 1,1,1,2,2,3,2,4,3,5,3,6,4,7,4,8,5,9,5,10,6,11,6,12,7,13,7,14,8,15,8,

%T 16,9,17,9,18,10,19,10,20,11,21,11,22,12,23,12,24,13,25,13,26,14,27,

%U 14,28,15,29,15,30,16,31,16,32,17,33,17,34,18,35,18,36,19,37,19,38,20,39,20

%N When dealing cards into 3 piles (Left, Center, Right), the number of cards in the n-th card's pile, if dealing in a pattern L, C, R, C, L, C, R, C, L, C, ... [as any thoughtful six-year-old will try to do when sharing a pile of candy among 3 people].

%C A008619 and A000027 interleaved; abs(a(n+1) - a(n)) = A059169(n). - _Reinhard Zumkeller_, Nov 15 2014

%H Reinhard Zumkeller, <a href="/A178804/b178804.txt">Table of n, a(n) for n = 1..10000</a>

%H "TwoPi", <a href="http://threesixty360.wordpress.com/2010/06/15/a-cool-sequence-problem/">A Cool Sequence Problem</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,-1).

%F a(n) = ceiling(n/4) if n is odd, n/2 if n is even.

%F From _R. J. Mathar_, Jun 19 2010: (Start)

%F a(n) = a(n-2) + a(n-4) - a(n-6).

%F G.f.: x*(1+x+x^3) / ( (1+x^2)*(x-1)^2*(1+x)^2 ). (End)

%F a(n) = (3n+1-2(-1)^((n+3+(1-n)(-1)^n)/4)+(n-3)(-1)^n)/8. - _Wesley Ivan Hurt_, Mar 19 2015

%t CoefficientList[Series[x*(1+x+x^3)/((1+x^2)*(x-1)^2*(1+x)^2), {x,0,90}], x] (* _G. C. Greubel_, Jan 23 2019 *)

%o import Data.List (transpose)

%o a178804 n = a178804_list !! (n-1)

%o a178804_list = concat \$ transpose [a008619_list, a000027_list]

%o -- _Reinhard Zumkeller_, Nov 15 2014

%o (PARI) my(x='x+O('x^90)); Vec(x*(1+x+x^3)/((1+x^2)*(x-1)^2*(1+x)^2)) \\ _G. C. Greubel_, Jan 23 2019

%o (MAGMA) m:=90; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( x*(1+x+x^3)/((1+x^2)*(x-1)^2*(1+x)^2) )); // _G. C. Greubel_, Jan 23 2019

%o (Sage) a=(x*(1+x+x^3)/((1+x^2)*(x-1)^2*(1+x)^2)).series(x, 90).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Jan 23 2019

%Y Cf. A000027, A008619, A211520 (partial sums), A059169.

%K easy,nonn

%O 1,4

%A Mark McKinzie (mmckinzie(AT)sjfc.edu), Jun 15 2010

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)