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 A340525 Triangle read by rows: T(n,k) = A006218(n-k+1)*A002865(k-1), 1 <= k <= n. 3
 1, 3, 0, 5, 0, 1, 8, 0, 3, 1, 10, 0, 5, 3, 2, 14, 0, 8, 5, 6, 2, 16, 0, 10, 8, 10, 6, 4, 20, 0, 14, 10, 16, 10, 12, 4, 23, 0, 16, 14, 20, 16, 20, 12, 7, 27, 0, 20, 16, 28, 20, 32, 20, 21, 8, 29, 0, 23, 20, 32, 28, 40, 32, 35, 24, 12, 35, 0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: the sum of row n equals A006128(n), the total number of parts in all partitions of n. LINKS EXAMPLE Triangle begins:    1;    3,  0;    5,  0,  1;    8,  0,  3,  1;   10,  0,  5,  3,  2;   14,  0,  8,  5,  6,  2;   16,  0, 10,  8, 10,  6,  4;   20,  0, 14, 10, 16, 10, 12,  4;   23,  0, 16, 14, 20, 16, 20, 12,  7;   27,  0, 20, 16, 28, 20, 32, 20, 21,  8;   29,  0, 23, 20, 32, 28, 40, 32, 35, 24, 12;   35,  0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14; ... For n = 6 the calculation of every term of row 6 is as follows: -------------------------- k   A002865         T(6,k) -------------------------- 1      1   *  14   =  14 2      0   *  10   =   0 3      1   *   8   =   8 4      1   *   5   =   5 5      2   *   3   =   6 6      2   *   1   =   2 .           A006218 -------------------------- The sum of row 6 is 14 + 0 + 8 + 5 + 6 + 2 = 35, equaling A006128(6). CROSSREFS Mirror of A245095. Row sums give A006128 (conjectured). Columns 1, 3 and 4 are A006218. Column 2 gives A000004. Leading diagonal gives A002865. Cf. A135010, A138121, A221531, A336811, A339106, A340424, A340524, A340426. Sequence in context: A276833 A166586 A122274 * A003966 A123931 A058026 Adjacent sequences:  A340522 A340523 A340524 * A340526 A340527 A340528 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Jan 10 2021 STATUS approved

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)