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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. 7
 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, 0, 0, 3, 17, 72, 237, 728, 2187, 0, 0, 1, 17, 66, 232, 722, 2186, 6561, 0, 0, 1, 11, 66, 222, 716, 2179, 6560, 19683, 0, 0, 1, 11, 54, 222, 701, 2172, 6552, 19682, 59049 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Antidiagonals n = 0..50, flattened FORMULA A(n,k) = A(n-1,k) + A(n-1, floor(k/2)) + A(n-1, floor(k/3)), with A(0,0) = 1. T(n, k) = A(k, n-k). Sum_{k=0..n} A(n, k) = A000400(n). T(n, n) = A(n, 0) = A000244(n). - G. C. Greubel, Jun 18 2022 EXAMPLE Array begins as: 1, 0, 0, 0, 0, 0, 0, ...; 3, 2, 1, 0, 0, 0, 0, ...; 9, 8, 6, 4, 3, 3, 1, ...; 27, 26, 23, 20, 17, 17, 11, ...; 81, 80, 76, 72, 66, 66, 54, ...; 243, 242, 237, 232, 222, 222, 202, ...; 729, 728, 722, 716, 701, 701, 671, ...; Antidiagonal rows begin as: 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; 0, 0, 3, 17, 72, 237, 728, 2187; 0, 0, 1, 17, 66, 232, 722, 2186, 6561; MATHEMATICA 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[n_, k_]:= A[k, n-k]; Table[A[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 18 2022 *) PROG (SageMath) @CachedFunction def A(n, k): if (n==0): return 0^k else: return A(n-1, k) + A(n-1, (k//2)) + A(n-1, (k//3)) def T(n, k): return A(k, n-k) flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 18 2022 CROSSREFS Row sums are 6^n: A000400. Columns are A000244, A024023, A060188, A061981, A061982 twice, A061983 twice, etc. Cf. A000244, A061290, A061930, A061979, A061984, A061987. Sequence in context: A341905 A354905 A099095 * A059683 A030208 A209939 Adjacent sequences: A061977 A061978 A061979 * A061981 A061982 A061983 KEYWORD nonn,tabl AUTHOR Henry Bottomley, May 24 2001 STATUS approved

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Last modified September 18 01:35 EDT 2024. Contains 375995 sequences. (Running on oeis4.)