A233774 Total number of vertices in the first n rows of Sierpinski gasket, with a(0) = 1.

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

Offset

0,2

Links

Table of n, a(n) for n=0..53.

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: A369801 A310075 A347275 * A175313 A289387 A080518

Adjacent sequences: A233771 A233772 A233773 * A233775 A233776 A233777

Keyword

nonn

Author

Omar E. Pol, Dec 16 2013

Status

approved