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A194273 Concentric triangular numbers (see Comments lines for definition). 3
0, 1, 3, 6, 9, 12, 15, 19, 24, 30, 36, 42, 48, 55, 63, 72, 81, 90, 99, 109, 120, 132, 144, 156, 168, 181, 195, 210, 225, 240, 255, 271, 288, 306, 324, 342, 360, 379, 399, 420, 441, 462, 483, 505, 528, 552, 576, 600, 624, 649, 675, 702, 729, 756, 783, 811 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This can be interpreted as a cellular automaton on the infinite hexagonal net. The sequence gives the number of cells "ON" in the structure after n-th stage. A194272 gives the first differences. For a definition without words see the illustration of initial terms in the example section. For other concentric polygonal numbers see A194274, A194275 and A032528.

Also, row sums of an infinite square array T(n,k) in which column k lists 6*k-1 zeros followed by the numbers A008486 (see example).

LINKS

Table of n, a(n) for n=0..55.

Index entries for sequences related to cellular automata

FORMULA

G.f.: x/(1-3*x+3*x^2-3*x^4+3*x^5-x^6) = x/((1-x)^3*(1+x)*(1-x+x^2)).

EXAMPLE

Using the numbers A008486 we can write:

0, 1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36,...

0, 0, 0, 0, 0,  0,  0,  1,  3,  6,  9, 12, 15, 18,...

0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  1,...

And so on.

=========================================================

The sums of the columns give this sequence:

0, 1, 3, 6, 9, 12, 15, 19, 24, 30, 36, 42, 48, 55,...

...

Illustration of initial terms:

.                                              o

.                                 o           o o

.                      o         o o         o   o

.             o       o o       o   o       o     o

.      o     o o     o   o     o     o     o       o

. o   o o   o o o   o o o o   o o o o o   o o o o o o

.

. 1    3      6        9          12           15

.

.                                           o

.                        o                 o o

.       o               o o               o   o

.      o o             o   o             o     o

.     o   o           o     o           o   o   o

.    o     o         o   o   o         o   o o   o

.   o   o   o       o   o o   o       o   o o o   o

.  o         o     o           o     o             o

. o o o o o o o   o o o o o o o o   o o o o o o o o o

.

.       19               24                 30

CROSSREFS

Cf. A000217, A008486, A032528, A069131, A152751, A194272, A194274, A194275.

Sequence in context: A156242 A060293 A220657 * A123581 A187337 A184999

Adjacent sequences:  A194270 A194271 A194272 * A194274 A194275 A194276

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Aug 20 2011

STATUS

approved

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Last modified September 17 06:52 EDT 2019. Contains 327119 sequences. (Running on oeis4.)