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A305722
Crystal ball sequence for the lattice C_8.
2
1, 129, 2945, 29953, 187137, 845185, 3032705, 9173505, 24331777, 58161793, 127791489, 261902081, 506298625, 931299201, 1641303169, 2786931713, 4580166657, 7312946305, 11379709825, 17304414465, 25772582657, 37668968833, 54121468545, 76551925249
OFFSET
0,2
COMMENTS
Partial sums of A019564.
LINKS
R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, Annales de l'institut Fourier, Tome 49 (1999) no. 3 , p. 727-762.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9), for n>8.
a(n) = Sum_{k=0..8} binomial(16, 2k)*binomial(n+k, 8).
G.f.: (1 + 120*x + 1820*x^2 + 8008*x^3 + 12870*x^4 + 8008*x^5 + 1820*x^6 + 120*x^7 + x^8) / (1 - x)^9. - Colin Barker, Jun 09 2018
PROG
(PARI) {a(n) = sum(k=0, 8, binomial(16, 2*k)*binomial(n+k, 8))}
(PARI) Vec((1 + 120*x + 1820*x^2 + 8008*x^3 + 12870*x^4 + 8008*x^5 + 1820*x^6 + 120*x^7 + x^8) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Jun 09 2018
(GAP) b:=8;; List([0..25], n->Sum([0..b], k->Binomial(2*b, 2*k)*Binomial(n+k, b))); # Muniru A Asiru, Jun 09 2018
CROSSREFS
Sequence in context: A297493 A279640 A327337 * A189608 A168067 A232034
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 09 2018
STATUS
approved