A008396 Crystal ball sequence for A_10 lattice.

1, 111, 3191, 43561, 365751, 2181257, 10106977, 38619087, 126825227, 368750757, 970336269, 2349638259, 5303497629, 11272376259, 22745345019, 43859522037, 81262792557, 145325576067, 251806927307

Offset

0,2

Comments

Comment from T. D. Noe, Apr 29 2007: For the formula to produce this sequence, the five minus signs should be pluses and a 1 should be added: 46189/907200*n^10 + 46189/181440*n^9 + 89947/60480*n^8 + 493207/43200*n^6 + 4812379/181440*n^4 + 43461/2800*n^2 + 26741/6048*n^7 + 171457/8640*n^5 + 111683/4536*n^3 + 7381/1260*n + 1.

Comment from N. J. A. Sloane, May 04 2007: In that case I need to recheck both the formula and the values to see which is correct.

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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

a(n) = 1 + 11*n*(1+n)*(483120 + 797004*n + 1233596*n^2 + 953849*n^3 + 682786*n^4 + 258791*n^5 + 105859*n^6 + 16796*n^7 + 4199*n^8)/907200.

G.f.: (1 + 100*x + 2025*x^2 + 14400*x^3 + 44100*x^4 + 63504*x^5 + 44100*x^6 + 14400*x^7 + 2025*x^8 + 100*x^9 + x^10)/(1-x)^11. - Colin Barker, May 28 2012

Maple

seq(1 + 11*n*(1+n)*(483120 + 797004*n + 1233596*n^2 + 953849*n^3 + 682786*n^4 + 258791*n^5 + 105859*n^6 + 16796*n^7 + 4199*n^8)/907200, n=0..40);

Mathematica

CoefficientList[Series[(x^10+100x^9+2025x^8+14400x^7+44100x^6+63504x^5+44100x^4+14400x^3+2025x^2+100x+1)/(1-x)^11, {x, 0, 40}], x] (* or *)
LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {1, 111, 3191, 43561, 365751, 2181257, 10106977, 38619087, 126825227, 368750757, 970336269}, 40] (* Harvey P. Dale, Mar 15 2023 *)

Prog

(Magma) [1 +11*n*(1+n)*(483120 +797004*n +1233596*n^2 +953849*n^3 +682786*n^4 +258791*n^5 +105859*n^6 +16796*n^7 +4199*n^8)/907200: n in [0..40]]; // G. C. Greubel, May 29 2023
(SageMath)
def A008396(n): return 1 +11*n*(1+n)*(483120 +797004*n +1233596*n^2 +953849*n^3 +682786*n^4 +258791*n^5 +105859*n^6 +16796*n^7 +4199*n^8)/907200
[A008396(n) for n in range(41)] # G. C. Greubel, May 29 2023

Crossrefs

Sequence in context: A264466 A302384 A303105 * A332950 A302956 A232080

Adjacent sequences: A008393 A008394 A008395 * A008397 A008398 A008399

Keyword

nonn,easy

Author

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

Status

approved