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A236267
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a(n) = 8n^2 + 3n + 1.
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0
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1, 12, 39, 82, 141, 216, 307, 414, 537, 676, 831, 1002, 1189, 1392, 1611, 1846, 2097, 2364, 2647, 2946, 3261, 3592, 3939, 4302, 4681, 5076, 5487, 5914, 6357, 6816, 7291, 7782, 8289, 8812, 9351, 9906, 10477, 11064, 11667, 12286, 12921, 13572, 14239, 14922
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OFFSET
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0,2
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COMMENTS
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Positions a(n) of hexagonal numbers such that h(a(n)) = h(a(n)-1) + h(4*n+1), where h=A000384.
First bisection of A057029. The sequence contains infinitely many squares: 1, 676, 779689, 899760016, ... [Bruno Berselli, Jan 24 2014]
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LINKS
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Table of n, a(n) for n=0..43.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: -(6*x^2+9*x+1) / (x-1)^3. - Colin Barker, Jan 21 2014
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Colin Barker, Jan 21 2014
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EXAMPLE
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For n=5, A000384(a(5)) = 93096 = A000384(a(5)-1)+A000384(4*5+1) = 92235 + 861.
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MATHEMATICA
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Table[8 n^2 + 3 n + 1, {n, 0, 50}] (* Bruno Berselli, Jan 24 2014 *)
LinearRecurrence[{3, -3, 1}, {1, 12, 39}, 50] (* Harvey P. Dale, May 26 2019 *)
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PROG
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(PARI) Vec(-(6*x^2+9*x+1)/(x-1)^3 + O(x^100)) \\ Colin Barker, Jan 21 2014
(MAGMA) [8*n^2+3*n+1: n in [0..50]]; // Bruno Berselli, Jan 24 2014
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CROSSREFS
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Cf. A000384, A057029, A064225, A152948, A236257.
Sequence in context: A209872 A186779 A154266 * A119094 A226348 A139691
Adjacent sequences: A236264 A236265 A236266 * A236268 A236269 A236270
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KEYWORD
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nonn,easy
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AUTHOR
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Vladimir Shevelev, Jan 21 2014
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EXTENSIONS
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More terms from Colin Barker, Jan 21 2014
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STATUS
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approved
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