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 A008396 Crystal ball sequence for A_10 lattice. 4
 1, 111, 3191, 43561, 365751, 2181257, 10106977, 38619087, 126825227, 368750757, 970336269, 2349638259, 5303497629, 11272376259, 22745345019, 43859522037, 81262792557, 145325576067, 251806927307 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 22 21:28 EDT 2023. Contains 365531 sequences. (Running on oeis4.)