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 A233774 Total number of vertices in the first n rows of Sierpinski gasket, with a(0) = 1. 5
 1, 3, 6, 10, 15, 19, 25, 33, 42, 46, 52, 60, 70, 78, 90, 106, 123, 127, 133, 141, 151, 159, 171, 187, 205, 213, 225, 241, 261, 277, 301, 333, 366, 370, 376, 384, 394, 402, 414, 430, 448, 456, 468, 484, 504, 520, 544, 576, 610, 618, 630, 646, 666, 682 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS Eric Weisstein's World of Mathematics, Sierpinski Graph Wikipedia, Sierpinski triangle FORMULA a(2^k) = A067771(k), k >= 0. EXAMPLE Illustration of initial terms: ----------------------------------------------------- .          Diagram            n     A233775(n)   a(n) ----------------------------------------------------- .             *               0         1         1 .            /T\ .           *---*             1         2         3 .          /T\ /T\ .         *---*---*           2         3         6 .        /T\     /T\ .       *---*   *---*         3         4        10 .      /T\ /T\ /T\ /T\ .     *---*---*---*---*       4         5        15 .    /T\             /T\ .   *---*           *---*     5         4        19 . After five stages the number of "black" triangles in the structure is A006046(5) = 11. The total number of vertices is 19, so a(5) = 19. CROSSREFS Partial sums of A233775. Cf. A001316, A006046, A047999, A067771. Sequence in context: A310073 A310074 A310075 * A175313 A289387 A080518 Adjacent sequences:  A233771 A233772 A233773 * A233775 A233776 A233777 KEYWORD nonn AUTHOR Omar E. Pol, Dec 16 2013 STATUS approved

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Last modified January 21 15:20 EST 2019. Contains 319350 sequences. (Running on oeis4.)