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A008419 Crystal ball sequence for 9-dimensional cubic lattice. 4
1, 19, 181, 1159, 5641, 22363, 75517, 224143, 598417, 1462563, 3317445, 7059735, 14218905, 27298155, 50250765, 89129247, 152951073, 254831667, 413442773, 654862247, 1014889769, 1541911931, 2300409629, 3375210671, 4876601009, 6946419011, 9765268709 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

FORMULA

G.f.: (1+x)^9/(1-x)^10.

a(n) = (4*n^9+18*n^8+240*n^7+756*n^6+3612*n^5+7182*n^4+14360*n^3+14724*n^2+ 10134*n+2835)/2835 - Johannes W. Meijer, Jul 14 2013

a(0)=1, a(1)=19, a(2)=181, a(3)=1159, a(4)=5641, a(5)=22363, a(6)=75517, a(7)=224143, a(8)=598417, a(9)=1462563, a(n)=10*a(n-1)-45*a(n-2)+ 120*a(n-3)- 210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+ 10*a(n-9)- a(n-10). - Harvey P. Dale, Jul 25 2013

MATHEMATICA

CoefficientList[Series[(z + 1)^9/(z - 1)^10, {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 19, 181, 1159, 5641, 22363, 75517, 224143, 598417, 1462563}, 40] (* Harvey P. Dale, Jul 25 2013 *)

CROSSREFS

Cf. A001847, A001848, A001849.

Cf. A240876.

Sequence in context: A133740 A125382 A126540 * A211866 A327848 A034273

Adjacent sequences:  A008416 A008417 A008418 * A008420 A008421 A008422

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 24 17:43 EST 2021. Contains 341577 sequences. (Running on oeis4.)