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A174114
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Even central polygonal numbers (A193868) divided by 2.
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9
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1, 2, 8, 11, 23, 28, 46, 53, 77, 86, 116, 127, 163, 176, 218, 233, 281, 298, 352, 371, 431, 452, 518, 541, 613, 638, 716, 743, 827, 856, 946, 977, 1073, 1106, 1208, 1243, 1351, 1388, 1502, 1541, 1661, 1702, 1828, 1871, 2003, 2048, 2186, 2233, 2377, 2426, 2576
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refs;
listen;
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OFFSET
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1,2
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COMMENTS
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Central terms of A170950, seen as a triangle of rows with an odd number of terms.
Equivalently, numbers of the form m*(4*m+3)+1, where m = 0, -1, 1, -2, 2, -3, 3, ... [Bruno Berselli, Jan 05 2016]
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LINKS
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FORMULA
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a(n+3) - a(n+2) - a(n+1) + a(n) = A010696(n+1).
G.f. -x*(1+x+4*x^2+x^3+x^4) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Aug 18 2011
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MATHEMATICA
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(Select[PolygonalNumber@ Range@ 100, OddQ] + 1 )/2 (* Version 10.4, or *)
Rest@ CoefficientList[Series[-x (1 + x + 4 x^2 + x^3 + x^4)/((1 + x)^2 (x - 1)^3), {x, 0, 50}], x] (* Michael De Vlieger, Jun 30 2016 *)
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PROG
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CROSSREFS
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Cf. A033951: numbers of the form m*(4*m+3)+1 for nonnegative m.
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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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