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A143689
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a(n) = (3*n^2 - n + 2)/2.
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12
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1, 2, 6, 13, 23, 36, 52, 71, 93, 118, 146, 177, 211, 248, 288, 331, 377, 426, 478, 533, 591, 652, 716, 783, 853, 926, 1002, 1081, 1163, 1248, 1336, 1427, 1521, 1618, 1718, 1821, 1927, 2036, 2148, 2263, 2381, 2502, 2626, 2753, 2883, 3016, 3152, 3291
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OFFSET
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0,2
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COMMENTS
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Equals left border of triangle A033292.
Equals binomial transform of [1, 1, 3, 0, 0, 0, ...].
These might be called "trisected pentagonal numbers": A figurate pentagonal number is composed of three triangles, of which the central one is the largest, and the removal of the triangular frame (3*n) of the central triangle trisects the figure. This is reflected in the formula a(n) = A000326(n+1) - 3*n. See illustration in links. - John Elias, May 27 2022
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - a(n-2) + 3.
O.g.f.: (1-x+3*x^2)/((1-x)^3). - Eric Werley, Jun 27 2011
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MATHEMATICA
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Table[(3n^2-n+2)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 2, 6}, 50] (* Harvey P. Dale, May 05 2014 *)
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PROG
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(Haskell)
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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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EXTENSIONS
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STATUS
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approved
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