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A032528
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Concentric hexagonal numbers: floor( 3*n^2 / 2 ).
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31
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0, 1, 6, 13, 24, 37, 54, 73, 96, 121, 150, 181, 216, 253, 294, 337, 384, 433, 486, 541, 600, 661, 726, 793, 864, 937, 1014, 1093, 1176, 1261, 1350, 1441, 1536, 1633, 1734, 1837, 1944, 2053, 2166, 2281, 2400, 2521, 2646, 2773, 2904, 3037, 3174, 3313, 3456, 3601, 3750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Omar E. Pol, Aug 20 2011: (Start)
Also, cellular automaton on the hexagonal net. The sequence gives the number of "ON" cells in the structure after n-th stage. A007310 gives the first differences. For a definition without words see the illustration of initial terms in the example section. Note that the cells become intermittent. A083577 gives the primes of this sequences.
Also, A033581 and A003154 interleaved.
Also, row sums of an infinite square array T(n,k) in which column k lists 2*k-1 zeros followed by the numbers A008458 (see example).
(End)
Sequence found by reading the line from 0, in the direction 0, 1,... and the same line from 0, in the direction 0, 6,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Main axis perpendicular to A045943 in the same spiral. - Omar E. Pol, Sep 08 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for sequences related to cellular automata
Index to sequences with linear recurrences with constant coefficients, signature (2,0,-2,1).
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FORMULA
| G.f.: (x+4*x^2+x^3)/(1-2*x+2*x^3-x^4) = x*(1+4*x+x^2)/((1+x)*(1-x)^3). a(n) = +2*a(n-1) -2*a(n-3) +1*a(n-4). - Joerg Arndt, Aug 22 2011
a(n) = (6*n^2+(-1)^n-1)/4. - Bruno Berselli, Aug 22 2011
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EXAMPLE
| Contribution from Omar E. Pol, Aug 20 2011: (Start)
Using the numbers A008458 we can write:
0, 1, 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
0, 0, 0, 1, 6, 12, 18, 24, 30, 36, 42, ...
0, 0, 0, 0, 0, 1, 6, 12, 18, 24, 30, ...
0, 0, 0, 0, 0, 0, 0, 1, 6, 12, 18, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, ...
And so on.
===========================================
The sums of the columns give this sequence:
0, 1, 6, 13, 24, 37, 54, 73, 96, 121, 150, ...
...
Illustration of initial terms as concentric hexagons:
.
. 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 o o o
. o o o o o
.
. 1 6 13 24 37
.
(End)
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PROG
| (MAGMA) [Floor(3*n^2/2): n in [0..50]]; // Vincenzo Librandi, Aug 21 2011
(Haskell)
a032528 n = a032528_list !! n
a032528_list = scanl (+) 0 a007310_list
-- Reinhard Zumkeller, Jan 07 2012
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CROSSREFS
| Cf. A003154, A007310, A008458, A033581, A083577. - Omar E. Pol, Aug 20 2011.
Cf. A000326, A001318, A005449, A045943. - Omar E. Pol, Sep 08 2011
Cf. A032527, A195041. Column 6 of A195040. - Omar E. Pol, Sep 28 2011
Sequence in context: A054311 A183452 A194126 * A058535 A131833 A101736
Adjacent sequences: A032525 A032526 A032527 * A032529 A032530 A032531
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| New name (but with the original formula) and more terms a(41)-a(50) from Omar E. Pol, Aug 20 2011
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