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A033951
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Write 1,2,... in clockwise spiral; sequence gives numbers on positive x axis.
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57
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1, 8, 23, 46, 77, 116, 163, 218, 281, 352, 431, 518, 613, 716, 827, 946, 1073, 1208, 1351, 1502, 1661, 1828, 2003, 2186, 2377, 2576, 2783, 2998, 3221, 3452, 3691, 3938, 4193, 4456, 4727, 5006, 5293, 5588, 5891, 6202, 6521, 6848, 7183, 7526, 7877, 8236
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OFFSET
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0,2
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COMMENTS
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a(n) is the first term in a sum of 2*n + 1 consecutive integers that equals (2*n + 1)^3. - Patrick J. McNab, Dec 24 2016
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LINKS
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FORMULA
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a(n) = 4*n^2 + 3*n + 1.
G.f.: (1 + 5*x + 2*x^2)/(1-x)^3.
Equals A132774 * [1, 2, 3, ...]; = binomial transform of [1, 7, 8, 0, 0, 0, ...]. - Gary W. Adamson, Aug 28 2007
a(0)=1, a(1)=8, a(2)=23, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Feb 07 2015
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EXAMPLE
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Spiral begins:
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65--66--67--68--69--70--71--72--73
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64 37--38--39--40--41--42--43 74
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63 36 17--18--19--20--21 44 75
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62 35 16 5---6---7 22 45 76
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61 34 15 4 1 8 23 46 77
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60 33 14 3---2 9 24 47
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59 32 13--12--11--10 25 48
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58 31--30--29--28--27--26 49
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57--56--55--54--53--52--51--50
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 8, 23}, 60] (* Harvey P. Dale, Feb 07 2015 *)
CoefficientList[Series[(1 + 5 x + 2 x^2)/(1 - x)^3, {x, 0, 45}], x] (* Michael De Vlieger, Feb 12 2017 *)
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PROG
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(PARI) a(n)=4*n^2+3*n+1
(Python)
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CROSSREFS
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Sequences from spirals: A001107, A002939, A007742, A033951, A033952, A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Olivier Gorin (gorin(AT)roazhon.inra.fr)
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EXTENSIONS
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STATUS
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approved
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