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 A195040 Square array read by antidiagonals with T(n,k) = k*n^2/4+(k-4)*((-1)^n-1)/8, n>=0, k>=0. 24
 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 3, 2, 1, 0, 1, 4, 5, 3, 1, 0, 0, 7, 8, 7, 4, 1, 0, 1, 9, 13, 12, 9, 5, 1, 0, 0, 13, 18, 19, 16, 11, 6, 1, 0, 1, 16, 25, 27, 25, 20, 13, 7, 1, 0, 0, 21, 32, 37, 36, 31, 24, 15, 8, 1, 0, 1, 25, 41, 48, 49, 45, 37, 28, 17, 9, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS Also, if k >= 2 and m = 2*k, then column k lists the numbers of the form k*n^2 and the centered m-gonal numbers interleaved. Note that, if k >= 3, this is also a table of concentric polygonal numbers since column k lists the concentric k-gonal numbers. It appears that the first differences of column k are the numbers that are congruent to {1, k-1} mod k, if k >= 3. LINKS Muniru A Asiru, Rows n=0..100, flattened EXAMPLE Array begins: .  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,... .  1,   1,   1,   1,   1,   1,   1,   1,   1,   1,... .  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,... .  1,   3,   5,   7,   9,  11,  13,  15,  17,  19,... .  0,   4,   8,  12,  16,  20,  24,  28,  32,  36,... .  1,   7,  13,  19,  25,  31,  37,  43,  49,  55,... .  0,   9,  18,  27,  36,  45,  54,  63,  72,  81,... .  1,  13,  25,  37,  49,  61,  73,  85,  97, 109,... .  0,  16,  32,  48,  64,  80,  96, 112, 128, 144,... .  1,  21,  41,  61,  81, 101, 121, 141, 161, 181,... .  0,  25,  50,  75, 100, 125, 150, 175, 200, 225,... ... MAPLE A195040 := proc(n, k)         k*n^2/4+((-1)^n-1)*(k-4)/8 ; end proc: for d from 0 to 12 do         for k from 0 to d do                 printf("%d, ", A195040(d-k, k)) ;         end do: end do; # R. J. Mathar, Sep 28 2011 MATHEMATICA t[n_, k_] := k*n^2/4+(k-4)*((-1)^n-1)/8; Flatten[ Table[ t[n-k, k], {n, 0, 11}, {k, 0, n}]] (* Jean-François Alcover, Dec 14 2011 *) PROG (GAP) nmax:=13;; T:=List([0..nmax], n->List([0..nmax], k->k*n^2/4+(k-4)*((-1)^n-1)/8));; b:=List([2..nmax], n->OrderedPartitions(n, 2));; a:=Flat(List([1..Length(b)], i->List([1..Length(b[i])], j->T[b[i][j][2]][b[i][j][1]]))); # Muniru A Asiru, Jul 19 2018 CROSSREFS Rows: A000004, A000012, A001477, A005408, A008586, A016921, A008591, A017533, A008598. Columns: A000035, A004652, A000982, A077043, A000290, A032527, A032528, A195041, A077221, A195042, A195142, A195043, A195143, A195045, A195145, A195046, A195146, A195047, A195147, A195048, A195148, A195049, A195149, A195058, A195158. Sequence in context: A291759 A068494 A200726 * A250486 A316826 A256449 Adjacent sequences:  A195037 A195038 A195039 * A195041 A195042 A195043 KEYWORD nonn,tabl,easy AUTHOR Omar E. Pol, Sep 27 2011 STATUS approved

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Last modified November 19 13:16 EST 2018. Contains 317351 sequences. (Running on oeis4.)