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 A289762 Triangular array T(m,k) = (m+1-k)^2 + k - 1 with m (row) >= 1 and k (column) >= 1, read by rows. 1
 1, 1, 4, 2, 2, 4, 9, 5, 3, 3, 5, 9, 16, 10, 6, 4, 4, 6, 10, 16, 25, 17, 11, 7, 5, 5, 7, 11, 17, 25, 36, 26, 18, 12, 8, 6, 6, 8, 12, 18, 26, 36, 49, 37, 27, 19, 13, 9, 7, 7, 9, 13, 19, 27, 37, 49, 64, 50, 38, 28, 20, 14, 10, 8, 8, 10, 14, 20, 28, 38, 50, 64, 81, 65, 51, 39, 29, 21, 15, 11, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The n-th row is of length = max(2n, 1) and the row sum is (2n^3 + 6n^2 - 2n) / 3. Rows m = 2, 3, 5, 11, and 41 (Euler's lucky numbers) give the prime numbers generated by the famous polynomials, but twice each one between m^2. LINKS Miquel Cerda, Table of n, a(n) for n = 1..306 Miquel Cerda, Triangle rows 1..41 Miquel Cerda, Isosceles triangle Rows 1..41 FORMULA The formula that gives the integers in the m-th rows can be expressed using quadratic polynomials: for row m = 1, a(k) = k^2 - 3*k + 3 for row m = 2, a(k) = k^2 - 5*k + 8 for row m = 3, a(k) = k^2 - 7*k + 15 for row m = 4, a(k) = k^2 - 9*k + 24 for row m = 5, a(k) = k^2 - 11*k + 35 for row m = 6, a(k) = k^2 - 13*k + 48 etc. EXAMPLE The m-th row start and end: T(m,1) = m^2, ..., T(m,2m) = m^2. In general T(m,k) = T(m,2m+1-k). m\k    1     2     3     4     5     6     7     8     9     10 1      1,    1, 2      4,    2,    2,    4 3      9,    5,    3,    3,    5,    9 4      16,   10,   6,    4,    4,    6,    10,   16 5      25,   17,   11,   7,    5,    5,    7,    11,   17,   25 6      36,   26,   18,   12,   8,    6,    6,    8,    12,   18, ... 7      49,   37,   27,   19,   13,   9,    7,    7,    9,    13, ... 8      64,   50,   38,   28,   20,   14,   10,   8,    8,    10, ... 9      81,   65,   51,   39,   29,   21,   15,   11,   9,    9, ... 10     100,  82,   66,   52,   40,   30    22,   16,   12,   10, ... The T(m,k) sequence as an isosceles triangle:                                      1  1                                  4   2  2  4                              9   5   3  3  5  9                          16  10  6   4  4  6  10  16                      25  17  11  7   5  5  7  11  17  25                  36  26  18  12  8   6  6  8  12  18  26  36              49  37  27  19  13  9   7  7  9  13  19  27  37  49          64  50  38  28  20  14  10  8  8  1  14  20  28  38  50  64      81  65  51  39  29  21  15  11  9  9  11 15  21  29  39  51  65  81 100  82  66  52  40  30  22  16  12  10 10 12 16  22  30  40  52  66  82  100 MATHEMATICA Table[(m + 1 - k)^2 + k - 1, {m, 0, 10}, {k, 2 m}] /. {} -> {0} // Flatten (* Michael De Vlieger, Jul 12 2017 *) PROG (PARI) T(m, k) = (m+1-k)^2+k-1 \\ Charles R Greathouse IV, Jul 12 2017 CROSSREFS m(41, k+1) = A060566(n), left and right border gives A000290(n). Sequence in context: A322510 A021707 A126560 * A064213 A245518 A217462 Adjacent sequences:  A289759 A289760 A289761 * A289763 A289764 A289765 KEYWORD nonn,tabf,easy AUTHOR Miquel Cerda, Jul 12 2017 STATUS approved

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Last modified October 22 17:39 EDT 2019. Contains 328319 sequences. (Running on oeis4.)