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A305722
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Crystal ball sequence for the lattice C_8.
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2
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1, 129, 2945, 29953, 187137, 845185, 3032705, 9173505, 24331777, 58161793, 127791489, 261902081, 506298625, 931299201, 1641303169, 2786931713, 4580166657, 7312946305, 11379709825, 17304414465, 25772582657, 37668968833, 54121468545, 76551925249
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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