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A185508 Third accumulation array, T, of the natural number array A000027, by antidiagonals. 5


%S 1,5,6,16,29,21,41,89,99,56,91,219,295,259,126,182,469,705,755,574,

%T 252,336,910,1470,1765,1645,1134,462,582,1638,2786,3605,3780,3206,

%U 2058,792,957,2778,4914,6706,7595,7266,5754,3498,1287,1507,4488,8190,11634,13916,14406,12894,9690,5643,2002,2288,6963,13035,19110,23814,26068,25284,21510,15510,8723,3003,3367,10439,19965,30030,38640,44100

%N Third accumulation array, T, of the natural number array A000027, by antidiagonals.

%C See A144112 (and A185506) for the definition of accumulation array (aa). A185508=aa(aa(aa(A000027))).

%C Column 1: A000389.

%F T(n,k)=F*(4n^2+(5k+23)n+4k^2+3k+41), where

%F F=k(k+1)(k+2)n(n+1)(n+2)/2880.

%e Northwest corner:

%e 1.....5....16....41....91...182

%e 6....29....89...219...469...910

%e 21...99...295...705..1470..2786

%e 56..259...755..1765..3605..6706

%t h[n_,k_]:=k(k+1)(k+2)n(n+1)(n+2)*(4n^2+(5k+23)n+4k^2+3k+41)/2880;

%t TableForm[Table[h[n,k],{n,1,10},{k,1,15}]]

%t Table[h[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten

%Y Cf. A000027, A185506, A185507, A185509.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jan 29 2011

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Last modified November 25 05:50 EST 2015. Contains 264407 sequences.