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A209294
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a(n) = (7*n^2 - 7*n + 4)/2.
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2
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2, 9, 23, 44, 72, 107, 149, 198, 254, 317, 387, 464, 548, 639, 737, 842, 954, 1073, 1199, 1332, 1472, 1619, 1773, 1934, 2102, 2277, 2459, 2648, 2844, 3047, 3257, 3474, 3698, 3929, 4167, 4412, 4664, 4923, 5189, 5462
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OFFSET
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1,1
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COMMENTS
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a(n) is the sum of the n-th centered triangular number and n-th centered square number.
Difference of consecutive terms gives A008589 (multiples of 7).
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LINKS
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FORMULA
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a(n) = (7*n^2 - 7*n + 4) = 7*T(n) + 2 with T = A000217.
a(n) = a(-n+1) = 3*a(n-1)-3*a(n-2)+a(n-3). - Bruno Berselli, Jan 18 2013
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MATHEMATICA
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Table[(7*n^2 - 7*n + 4)/2, {n, 1, 50}] (* G. C. Greubel, Jan 04 2018 *)
LinearRecurrence[{3, -3, 1}, {2, 9, 23}, 40] (* Harvey P. Dale, Nov 02 2020 *)
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PROG
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(Magma) [(7*n^2 - 7*n + 4)/2: n in [1..30]]; // G. C. Greubel, Jan 04 2018
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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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