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A024204
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[ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.
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1
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0, 2, 4, 6, 10, 14, 19, 24, 30, 37, 44, 53, 61, 71, 81, 92, 103, 115, 128, 141, 156, 170, 186, 202, 219, 236, 254, 273, 292, 313, 333, 355, 377, 400, 423, 447, 472, 497, 524, 550, 578, 606, 635, 664, 694, 725, 756, 789, 821, 855, 889, 924, 959, 995, 1032
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OFFSET
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1,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).
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FORMULA
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a(n) = floor((n^4 + 5*n^3 + 7*n^2 + 2*n)/(3*n^2 + 11*n + 9)). - Neven Juric (neven.juric(AT)apis-it.hr), neven.juric(AT)apis-it.hr, May 17 2007
a(n) = floor((n^3 + 2*n^2)/(3*n + 2)). - Gary Detlefs, Jul 13 2010
G.f.: x^2*(x^11-2*x^10+2*x^9-x^8-x^7-x^5-2*x^3-2) / ((x-1)^3*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Aug 16 2014
For k > 0, a(9*k) = 27*k^2 + 4*k - 1, a(9*k+1) = 27*k^2 + 10*k, a(9*k+2) = 27*k^2 + 16*k + 1, a(9*k+3) = 27*k^2 + 22*k + 4, a(9*k+4) = 27*k^2 + 28*k + 6, a(9*k+5) = 27*k^2 + 34*k + 10, a(9*k+6) = 27*k^2 + 40*k + 14, a(9*k+7) = 27*k^2 + 46*k + 19, a(9*k+8) = 27*k^2 + 52*k + 24. - Jinyuan Wang, Jul 09 2020
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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