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 A338758 a(n) is the sum of even-indexed terms (of every row) of first n rows of the triangle A237591. 3
 0, 0, 1, 2, 4, 5, 7, 9, 11, 14, 18, 21, 25, 30, 34, 38, 43, 48, 54, 59, 65, 72, 80, 87, 94, 102, 111, 119, 128, 136, 145, 154, 164, 175, 185, 195, 206, 218, 231, 243, 256, 268, 281, 295, 308, 322, 337, 351, 365, 379, 394, 410, 427, 443, 460, 476, 493, 511, 530, 548, 567, 587, 606, 625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS FORMULA a(n) = A000217(n) - A338204(n). EXAMPLE Illustration of a(16) = 38 in two ways: . Level 1 2                            _                                      _ 3                           |_|                                   _|_| 4                          _|_|                                 _|_| 5                         |_ _|                               _|_ _| 6                        _|_|                               _|_| 7                       |_ _|                             _|_ _| 8                      _|_ _|                           _|_ _| 9                     |_ _|  _                        _|_ _| 10                   _|_ _| |_|                     _|_ _|_| 11                  |_ _ _| |_|                   _|_ _ _|_| 12                 _|_ _|   |_|                 _|_ _|_| 13                |_ _ _|  _|_|               _|_ _ _|_| 14               _|_ _ _| |_ _|             _|_ _ _|_ _| 15              |_ _ _|   |_|             _|_ _ _|_| 16              |_ _ _|   |_|            |_ _ _|_| ...                     Figure 1.                       Figure 2. . For n = 16, figure 1 shows the illustration of a(16) taken from the isosceles triangle of A237593. There are 38 cells in the first 16 levels of the diagram, so a(16) = 38. Figure 2 shows the illustration of a(16) taken from an octant of the pyramid described in A244050 and A245092. There are 38 cells in the first 16 levels of the diagram, so a(16) = 38. PROG (PARI) row235791(n) = vector((sqrtint(8*n+1)-1)\2, i, 1+(n-(i*(i+1)/2))\i); row237591(n) = {my(orow = concat(row235791(n), 0)); vector(#orow -1, i, orow[i] - orow[i+1]); } a003056(n) = floor((sqrt(1+8*n)-1)/2); a322141(n) = my(row=row237591(n)); sum(k=1, a003056(n), if (!(k%2), row[k])); a(n) = sum(k=1, n, a322141(k)); \\ Michel Marcus, Dec 22 2020 CROSSREFS Partial sums of A322141. Cf. A000217, A067742, A237591, A237593, A240542, A259177, A286001, A338204. Sequence in context: A186388 A058577 A071917 * A051060 A116650 A140205 Adjacent sequences:  A338755 A338756 A338757 * A338759 A338760 A338761 KEYWORD nonn AUTHOR Omar E. Pol, Dec 21 2020 STATUS approved

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Last modified April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)