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A160999 Row sums of A027052. 2

%I

%S 1,2,5,12,31,84,233,656,1865,5338,15355,44342,128455,373100,1086087,

%T 3167634,9254009,27074666,79316491,232633206,683026535,2007327660,

%U 5904415195,17381265934,51203990457,150945252394,445252685313

%N Row sums of A027052.

%H G. C. Greubel, <a href="/A160999/b160999.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{k=0..2*n} A027052(n,k).

%F Conjecture: (-n+2)*a(n) +(6*n-11)*a(n-1) +(-7*n+1)*a(n-2) +2*(-4*n+27)*a(n-3) +(5*n-28)*a(n-4) +(2*n-3)*a(n-5) +3*(n-5)*a(n-6)=0. - _R. J. Mathar_, May 26 2016

%e a(2) = 1+0+1+2+1 = 5.

%e a(3) = 1+0+1+2+3+4+1 = 12.

%p A027052 := proc(n,k) option remember; if k =0 or k = 2*n then 1; elif k = 1 then 0; elif k =2 then 1; else procname(n-1,k-3)+procname(n-1,k-2)+procname(n-1,k-1) ; fi; end:

%p A160999 := proc(n) add( A027052(n,k),k=0..2*n) ; end: seq(A160999(n),n=0..30) ;

%t T[n_, k_]:= T[n, k]= If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n, k], {k,0,2*n}], {n,0,30}] (* _G. C. Greubel_, Nov 06 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o if (k==0 or k==2 or k==2*n): return 1

%o elif (k==1): return 0

%o else: return sum(T(n-1, k-j) for j in (1..3))

%o [sum(T(n, k) for k in (0..2*n)) for n in (0..30)] # _G. C. Greubel_, Nov 06 2019

%K easy,nonn

%O 0,2

%A _R. J. Mathar_, Jun 01 2009

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Last modified July 5 18:57 EDT 2020. Contains 335473 sequences. (Running on oeis4.)