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A157286
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a(n) = 36*n^2 - n.
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4
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35, 142, 321, 572, 895, 1290, 1757, 2296, 2907, 3590, 4345, 5172, 6071, 7042, 8085, 9200, 10387, 11646, 12977, 14380, 15855, 17402, 19021, 20712, 22475, 24310, 26217, 28196, 30247, 32370, 34565, 36832, 39171, 41582, 44065, 46620, 49247, 51946
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OFFSET
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1,1
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COMMENTS
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The identity (10368*n^2 - 288*n + 1)^2 - (36*n^2 - n)*(1728*n - 24)^2 = 1 can be written as A157288(n)^2 - a(n)*A157287(n)^2 = 1; this is the case s=6 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1.
Also, the identity (72*n - 1)^2 - (36*n^2 - n)*12^2 = 1 can be written as A157921(n)^2 - a(n)*12^2 = 1 (see Barbeau's paper). (End)
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(37*x + 35)/(1-x)^3.
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {35, 142, 321}, 40] (* Vincenzo Librandi, Jan 28 2012 *)
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PROG
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(Magma) [36*n^2-n: n in [1..40]]
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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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