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A061980 Square array A(n,k) = A(n-1,k) + A(n-1, floor(k/2)) + A(n-1, floor(k/3)), with A(0,0) = 1, read by antidiagonals.

%I A061980 #7 Jun 19 2022 02:20:48
%S A061980 1,0,3,0,2,9,0,1,8,27,0,0,6,26,81,0,0,4,23,80,243,0,0,3,20,76,242,729,
%T A061980 0,0,3,17,72,237,728,2187,0,0,1,17,66,232,722,2186,6561,0,0,1,11,66,
%U A061980 222,716,2179,6560,19683,0,0,1,11,54,222,701,2172,6552,19682,59049
%N A061980 Square array A(n,k) = A(n-1,k) + A(n-1, floor(k/2)) + A(n-1, floor(k/3)), with A(0,0) = 1, read by antidiagonals.
%H A061980 G. C. Greubel, <a href="/A061980/b061980.txt">Antidiagonals n = 0..50, flattened</a>
%F A061980 A(n,k) = A(n-1,k) + A(n-1, floor(k/2)) + A(n-1, floor(k/3)), with A(0,0) = 1.
%F A061980 T(n, k) = A(k, n-k).
%F A061980 Sum_{k=0..n} A(n, k) = A000400(n).
%F A061980 T(n, n) = A(n, 0) = A000244(n). - _G. C. Greubel_, Jun 18 2022
%e A061980 Array begins as:
%e A061980     1,   0,   0,   0,   0,   0,   0, ...;
%e A061980     3,   2,   1,   0,   0,   0,   0, ...;
%e A061980     9,   8,   6,   4,   3,   3,   1, ...;
%e A061980    27,  26,  23,  20,  17,  17,  11, ...;
%e A061980    81,  80,  76,  72,  66,  66,  54, ...;
%e A061980   243, 242, 237, 232, 222, 222, 202, ...;
%e A061980   729, 728, 722, 716, 701, 701, 671, ...;
%e A061980 Antidiagonal rows begin as:
%e A061980   1;
%e A061980   0, 3;
%e A061980   0, 2, 9;
%e A061980   0, 1, 8, 27;
%e A061980   0, 0, 6, 26, 81;
%e A061980   0, 0, 4, 23, 80, 243;
%e A061980   0, 0, 3, 20, 76, 242, 729;
%e A061980   0, 0, 3, 17, 72, 237, 728, 2187;
%e A061980   0, 0, 1, 17, 66, 232, 722, 2186, 6561;
%t A061980 A[n_, k_]:= A[n, k]= If[n==0, Boole[k==0], A[n-1,k] +A[n-1,Floor[k/2]] +A[n-1, Floor[k/3]]];
%t A061980 T[n_, k_]:= A[k, n-k];
%t A061980 Table[A[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jun 18 2022 *)
%o A061980 (SageMath)
%o A061980 @CachedFunction
%o A061980 def A(n,k):
%o A061980     if (n==0): return 0^k
%o A061980     else: return A(n-1, k) + A(n-1, (k//2)) + A(n-1, (k//3))
%o A061980 def T(n, k): return A(k, n-k)
%o A061980 flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 18 2022
%Y A061980 Row sums are 6^n: A000400.
%Y A061980 Columns are A000244, A024023, A060188, A061981, A061982 twice, A061983 twice, etc.
%Y A061980 Cf. A000244, A061290, A061930, A061979, A061984, A061987.
%K A061980 nonn,tabl
%O A061980 0,3
%A A061980 _Henry Bottomley_, May 24 2001