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A008400 Crystal ball sequence for E_6 lattice. 1
1, 73, 1135, 7831, 34147, 111835, 301645, 707365, 1492669, 2900773, 5276899, 9093547, 14978575, 23746087, 36430129, 54321193, 79005529, 112407265, 156833335, 215021215, 290189467, 386091091 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

LINKS

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

Index entries for crystal ball sequences

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 linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

a(n) = 39/10*n^6+117/10*n^5+75/4*n^4+18*n^3+267/20*n^2+63/10*n+1 (see Maple lines).

G.f.: (1+66*x+645*x^2+1384*x^3+645*x^4+66*x^5+x^6)/(1-x)^7. [Colin Barker, Mar 16 2012]

a(0)=1, a(1)=73, a(2)=1135, a(3)=7831, a(4)=34147, a(5)=111835, a(6)=301645, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+ a(n-7). - Harvey P. Dale, Feb 23 2015

MAPLE

39/10*n^6+117/10*n^5+75/4*n^4+18*n^3+267/20*n^2+63/10*n+1;

MATHEMATICA

Table[39/10 n^6+117/10 n^5+75/4 n^4+18n^3+267/20 n^2+63/10 n+1, {n, 0, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 73, 1135, 7831, 34147, 111835, 301645}, 30] (* Harvey P. Dale, Feb 23 2015 *)

PROG

(PARI) a(n)=(78*n^6 + 234*n^5 + 375*n^4 + 360*n^3 + 267*n^2 + 126*n + 20)/20 \\ Charles R Greathouse IV, Feb 10 2017

CROSSREFS

Sequence in context: A320205 A305549 A320214 * A090685 A232297 A008392

Adjacent sequences:  A008397 A008398 A008399 * A008401 A008402 A008403

KEYWORD

nonn,easy,nice

AUTHOR

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

STATUS

approved

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Last modified March 19 04:18 EDT 2019. Contains 321311 sequences. (Running on oeis4.)