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A332243
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Starhex honeycomb numbers: a(n) = 13 + 60*n + 60*n^2.
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2
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13, 133, 373, 733, 1213, 1813, 2533, 3373, 4333, 5413, 6613, 7933, 9373, 10933, 12613, 14413, 16333, 18373, 20533, 22813, 25213, 27733, 30373, 33133, 36013, 39013, 42133, 45373, 48733, 52213, 55813, 59533, 63373, 67333, 71413, 75613, 79933, 84373
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OFFSET
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0,1
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REFERENCES
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M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 20.
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LINKS
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FORMULA
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a(n) = 12*(5*n*(n + 1) + 1) + 1.
O.g.f.: (13 + 94*x + 13*x^2)/(1 - x)^3.
E.g.f.: exp(x)*(13 + 120*x + 60*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-2) for n > 2. (End)
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EXAMPLE
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Example: a(2) = 13 + 60*2 + 60*2^2 = 373.
Illustration of initial terms:
. 0
. 0 0 0 0
. 0 0 0
. 0 0 0 0 0 0
. 0 0 0 0 * * 0 * * 0 0 0 0
. 0 0 0 * * * * * * 0 0 0
. 0 0 0 0 * * 0 * * 0 0 0 0
. 0 * * 0 0 0 0 * * 0
. * * * 0 0 0 * * *
. 0 * * 0 0 0 0 * * 0
. 0 0 0 0 * * 0 * * 0 0 0 0
. 0 0 0 * * * * * * 0 0 0
. 0 0 0 0 0 * * 0 * * 0 0 0 0
. 0 * * 0 0 0 0 0 0 0
. * 0 * 0 0 0
. 0 * * 0 0 0 0 0
. 0 0
.
. 13 133
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {13, 133, 373}, 40] (* Harvey P. Dale, Nov 18 2023 *)
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PROG
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CROSSREFS
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Subsequence of A082369: cf. formula.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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