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A106595 Triangle read by rows: odd-numbered rows of A106580.

%I A106595 #12 Sep 08 2021 01:27:46
%S A106595 1,1,1,2,3,3,1,2,5,9,12,12,1,2,5,13,26,41,53,53,1,2,5,13,34,73,129,
%T A106595 194,247,247,1,2,5,13,34,89,201,386,645,945,1192,1192,1,2,5,13,34,89,
%U A106595 233,546,1117,2021,3266,4705,5897,5897,1,2,5,13,34,89,233,610,1469,3157,6082,10593,16737,23826,29723,29723
%N A106595 Triangle read by rows: odd-numbered rows of A106580.
%H A106595 G. C. Greubel, <a href="/A106595/b106595.txt">Rows n = 0..50 of the irregular triangle, flattened</a>
%F A106595 T(n, k) = A106580(2*n+1, k).
%e A106595 Irregular triangle begins as:
%e A106595   1, 1;
%e A106595   1, 2, 3,  3;
%e A106595   1, 2, 5,  9, 12, 12;
%e A106595   1, 2, 5, 13, 26, 41,  53,  53;
%e A106595   1, 2, 5, 13, 34, 73, 129, 194,  247,  247;
%e A106595   1, 2, 5, 13, 34, 89, 201, 386,  645,  945, 1192, 1192;
%e A106595   1, 2, 5, 13, 34, 89, 233, 546, 1117, 2021, 3266, 4705, 5897, 5897;
%p A106595 A106580 := proc(n,k) option remember ; if k =0 then 1 ; else A106580(n,k-1)+add(A106580(n-2*i,k-i),i=1..min(k,floor(n/2),n-k)) ; fi ; end: for n from 1 to 13 by 2 do for k from 0 to n do printf("%d, ",A106580(n,k)) ; od ; od ; # _R. J. Mathar_, May 02 2007
%t A106595 T[n_, k_]:= T[n, k]= If[k==0, 1, T[n, k-1] + Sum[T[n-2*j, k-j], {j, 1, Min[k, Floor[n/2], n-k]}]]; (* T(n, k) = A106580; T(2*n+1, k) = A106595 *)
%t A106595 Table[T[2*n+1, k], {n, 0, 12}, {k, 0, 2*n+1}]//Flatten (* _G. C. Greubel_, Sep 08 2021 *)
%o A106595 (Sage)
%o A106595 @CachedFunction
%o A106595 def T(n, k): # T(n, k) = A106580; T(2*n+1, k) = A106595
%o A106595     if (k<0): return 0
%o A106595     elif (k==0): return 1
%o A106595     else: return T(n, k-1) + sum( T(n-2*j, k-j) for j in (1..min(k, n//2, n-k)))
%o A106595 flatten([[T(2*n+1, k) for k in (0..2*n+1)] for n in (0..12)]) # _G. C. Greubel_, Sep 08 2021
%Y A106595 Cf. A106580, A106585.
%K A106595 nonn,tabf,easy
%O A106595 0,4
%A A106595 _N. J. A. Sloane_, May 30 2005
%E A106595 More terms from _R. J. Mathar_, May 02 2007