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A063436 Write 1,2,3,4,... counterclockwise in a hexagonal spiral around 0 starting left down, then a(n) is the sequence found by reading from 0 in the vertical upward direction. 2
0, 15, 54, 117, 204, 315, 450, 609, 792, 999, 1230, 1485, 1764, 2067, 2394, 2745, 3120, 3519, 3942, 4389, 4860, 5355, 5874, 6417, 6984, 7575, 8190, 8829, 9492, 10179, 10890, 11625, 12384, 13167, 13974, 14805, 15660, 16539, 17442, 18369 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Related to parity of Beatty sequences for exp(-(1/2)/n). Let f(k,n)=-sum(i=1,n,sum(j=1,i,(-1)^floor(j*exp(-(1/2)/n)))), then a(n)=Max{f(k,n) : 1<=k<=4*a(n)-2} and for 0<=i<=4*a(n)-3, f(i,n)=f(4*a(n)-2-i,n). - Benoit Cloitre, May 26 2004

Or, sum of multiples of 2 and 3 from 0 to 6n. - Zak Seidov, Aug 06 2016

REFERENCES

B. Cloitre, On parity properties of certain Beatty sequences, in preparation 2004

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 3*n*(4*n+1) = 3*A007742(n).

a(n) = 24*n + a(n-1) - 9 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

From Colin Barker, Jul 07 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: 3*x*(5+3*x)/(1-x)^3. (End)

EXAMPLE

The spiral begins:

.

        16--15--14

        /         \

      17   5---4  13

      /   /     \   \

    18   6   0   3  12

    /   /   /   /   /

  19   7   1---2  11  26

    \   \         /   /

    20   8---9--10  25

      \             /

      21--22--23--24

PROG

(PARI) { for (n=0, 1000, write("b063436.txt", n, " ", n*(12*n + 3)) ) } \\ Harry J. Smith, Aug 21 2009

CROSSREFS

Cf. A062783, A000567.

Sequence in context: A194454 A219384 A198955 * A010004 A172073 A059145

Adjacent sequences:  A063433 A063434 A063435 * A063437 A063438 A063439

KEYWORD

nonn,easy

AUTHOR

Floor van Lamoen, Jul 21 2001

STATUS

approved

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Last modified April 25 13:31 EDT 2019. Contains 322461 sequences. (Running on oeis4.)