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A007202 Crystal ball sequence for hexagonal close-packing.
(Formerly M4899)
5
1, 13, 57, 153, 323, 587, 967, 1483, 2157, 3009, 4061, 5333, 6847, 8623, 10683, 13047, 15737, 18773, 22177, 25969, 30171, 34803, 39887, 45443, 51493, 58057, 65157, 72813, 81047, 89879, 99331, 109423, 120177, 131613, 143753, 156617 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Index entries for crystal ball sequences

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

FORMULA

Nearest integer to (7/8)*( (n+1)^4 - n^4 ).

G.f.: (x^4+10*x^3+20*x^2+10*x+1)/(x-1)^4/(x+1).

a(n) = 7*(2*n+1)*(2*n^2+2*n+1)/8 +(-1)^n/8. - R. J. Mathar, Mar 24 2011

a(0)=1, a(1)=13, a(2)=57, a(3)=153, a(4)=323, a(n)=3*a(n-1)- 2*a(n-2)- 2*a(n-3)+3*a(n-4)-a(n-5) [From Harvey P. Dale, Jul 15 2011]

MATHEMATICA

Table[Floor[(7((n+1)^4-n^4)+4)/8], {n, 0, 40}] (* or *) LinearRecurrence[ {3, -2, -2, 3, -1}, {1, 13, 57, 153, 323}, 40] (* Harvey P. Dale, Jul 15 2011 *)

PROG

(PARI) j=[]; for(n=0, 75, j=concat(j, round((7/8)*((n+1)^4-n^4)))); j

CROSSREFS

Sequence in context: A212053 A264853 A210290 * A222161 A218593 A212405

Adjacent sequences:  A007199 A007200 A007201 * A007203 A007204 A007205

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane and J. H. Conway

EXTENSIONS

More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jul 14 2001

STATUS

approved

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Last modified December 10 23:13 EST 2016. Contains 279021 sequences.