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A276819
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a(n) = (9*n^2 - n)/2 + 1.
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3
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1, 5, 18, 40, 71, 111, 160, 218, 285, 361, 446, 540, 643, 755, 876, 1006, 1145, 1293, 1450, 1616, 1791, 1975, 2168, 2370, 2581, 2801, 3030, 3268, 3515, 3771, 4036, 4310, 4593, 4885, 5186, 5496, 5815, 6143, 6480, 6826, 7181, 7545, 7918, 8300, 8691, 9091, 9500, 9918, 10345, 10781, 11226, 11680, 12143, 12615
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OFFSET
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0,2
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COMMENTS
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First differences are given by A017209.
72*a(n) - 71 is a perfect square. - Klaus Purath, Jan 14 2022
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LINKS
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FORMULA
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a(n) = (9*n^2 - n)/2 + 1.
a(n) = a(n-1) + 9*n - 5 with a(0) = 1.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: (1 + 2*x + 6*x^2)/(1 - x)^3. (End)
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MATHEMATICA
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Table[(9*n^2-n)/2+1, {n, 0, 100}]
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PROG
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(PARI) Vec((1+2*x+6*x^2)/(1-x)^3 + O(x^60)) \\ Colin Barker, Sep 18 2016
(PARI) a(n) = (9*n^2 - n)/2 + 1; \\ Altug Alkan, Sep 18 2016
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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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