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A350924
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a(0) = 1, a(1) = 3, and a(n) = 16*a(n-1) - a(n-2) - 4 for n >= 2.
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9
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1, 3, 43, 681, 10849, 172899, 2755531, 43915593, 699893953, 11154387651, 177770308459, 2833170547689, 45152958454561, 719614164725283, 11468673677149963, 182779164669674121, 2912997961037635969, 46425188211932501379, 739890013429882386091, 11791815026666185676073
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OFFSET
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0,2
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COMMENTS
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One of 10 linear second-order recurrence sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4 and together forming A350916.
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LINKS
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FORMULA
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G.f.: (1 - 14*x + 9*x^2)/((1 - x)*(1 - 16*x + x^2)). - Stefano Spezia, Jan 22 2022
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MATHEMATICA
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nxt[{a_, b_}]:={b, 16b-a-4}; NestList[nxt, {1, 3}, 20][[All, 1]] (* or *) LinearRecurrence[ {17, -17, 1}, {1, 3, 43}, 20] (* Harvey P. Dale, Jan 08 2023 *)
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PROG
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(Python)
a350924 = [1, 3]
for k in range(2, 100): a350924.append(16*a350924[k-1]-a350924[k-2]-4)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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