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 A322744 Array T(n,k) = (3*n*k - A319929(n,k))/2, n >= 1, k >= 1, read by antidiagonals. 11
 1, 2, 2, 3, 6, 3, 4, 8, 8, 4, 5, 12, 11, 12, 5, 6, 14, 16, 16, 14, 6, 7, 18, 19, 24, 19, 18, 7, 8, 20, 24, 28, 28, 24, 20, 8, 9, 24, 27, 36, 33, 36, 27, 24, 9, 10, 26, 32, 40, 42, 42, 40, 32, 26, 10, 11, 30, 35, 48, 47, 54, 47, 48, 35, 30, 11, 12, 32, 40, 52, 56, 60, 60, 56, 52, 40, 32, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Associative multiplication-like table whose values depend on whether n and k are odd or even. Associativity is proved by checking the formula with eight cases of three odd and even arguments. T(n,k) is distributive as long as partitioning an even number into two odd numbers is not allowed. LINKS David Lovler, Table of n, a(n) for n = 1..861 (Antidiagonals n = 1..41, flattened) FORMULA T(n,k) = (3*n*k - (n + k - 1))/2, if n is odd and k is odd; T(n,k) = (3*n*k - n)/2, if n is even and k is odd; T(n,k) = (3*n*k - k)/2, if n is odd and k is even; T(n,k) = 3*n*k/2, if n is even and k is even. T(n,k) = (3*n*k - A319929(n,k))/2. T(n,k) = 6*floor(n/2)*floor(k/2) + A319929(n,k). EXAMPLE Array T(n,k) begins:    1   2   3   4   5   6   7   8   9  10 ...    2   6   8  12  14  18  20  24  26  30 ...    3   8  11  16  19  24  27  32  35  40 ...    4  12  16  24  28  36  40  48  52  60 ...    5  14  19  28  33  42  47  56  61  70 ...    6  18  24  36  42  54  60  72  78  90 ...    7  20  27  40  47  60  67  80  87 100 ...    8  24  32  48  56  72  80  96 104 120 ...    9  26  35  52  61  78  87 104 113 130 ...   10  30  40  60  70  90 100 120 130 150 ...   ... MATHEMATICA Table[Function[n, (3 n k - If[OddQ@ n, If[OddQ@ k, n + k - 1, k], If[OddQ@ k, n, 0]])/2][m - k + 1], {m, 12}, {k, m}] // Flatten (* Michael De Vlieger, Apr 21 2019 *) PROG (PARI) T319929(n, k) = if (n%2, if (k%2, n+k-1, k), if (k%2, n, 0)); T(n, k) = (3*n*k - T319929(n, k))/2; matrix(6, 6, n, k, T(n, k)) \\ Michel Marcus, Dec 27 2018 CROSSREFS Equals A003991 + A322630 - A319929. Cf. A327263, A307001, A307002, A340746, A340747. Sequence in context: A291372 A064426 A051173 * A128228 A190098 A272973 Adjacent sequences:  A322741 A322742 A322743 * A322745 A322746 A322747 KEYWORD nonn,tabl,easy AUTHOR David Lovler, Dec 24 2018 STATUS approved

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Last modified August 5 01:51 EDT 2021. Contains 346456 sequences. (Running on oeis4.)