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A330451
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a(n) = a(n-3) + 20*n - 30 for n > 2, with a(0)=0, a(1)=3, a(2)=13.
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1
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0, 3, 13, 30, 53, 83, 120, 163, 213, 270, 333, 403, 480, 563, 653, 750, 853, 963, 1080, 1203, 1333, 1470, 1613, 1763, 1920, 2083, 2253, 2430, 2613, 2803, 3000, 3203, 3413, 3630, 3853, 4083, 4320, 4563, 4813, 5070
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OFFSET
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0,2
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COMMENTS
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Main N-S vertical in the pentagonal spiral for A002264:
16
16 10 10
16 9 5 5 10
15 9 4 1 2 5 11
15 9 4 1 0 0 2 6 11
15 8 4 1 0 2 6 11
14 8 3 3 3 6 12
14 8 7 7 7 12
14 13 13 13 12
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LINKS
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FORMULA
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G.f.: x*(1 + x)*(3 + 4*x + 3*x^2) / ((1 - x)^3*(1 + x + x^2)). - Colin Barker, Mar 02 2020
a(n) = a(-n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).
a(n) = (2/9)*(-1 + 15*n^2 + cos(2*n*Pi/3)). - Stefano Spezia, Mar 02 2020
a(3*n) = 30*n^2.
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MATHEMATICA
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Table[2/9(-1+15n^2+Cos[2n*Pi/3]), {n, 0, 39}] (* Stefano Spezia, Mar 02 2020 *)
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PROG
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(PARI) concat(0, Vec(x*(1 + x)*(3 + 4*x + 3*x^2) / ((1 - x)^3*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Mar 02 2020
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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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