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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

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: A029716 A284521 A162553 * A175313 A080518 A078594

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 June 23 16:45 EDT 2017. Contains 288666 sequences.