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A175822
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Partial sums of ceiling(n^2/7).
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4
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0, 1, 2, 4, 7, 11, 17, 24, 34, 46, 61, 79, 100, 125, 153, 186, 223, 265, 312, 364, 422, 485, 555, 631, 714, 804, 901, 1006, 1118, 1239, 1368, 1506, 1653, 1809, 1975, 2150, 2336, 2532, 2739, 2957, 3186, 3427, 3679, 3944, 4221, 4511, 4814, 5130, 5460, 5803, 6161
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OFFSET
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0,3
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,1,-3,3,-1).
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FORMULA
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a(n) = round((2*n+1)*(n^2 + n + 12)/42).
a(n) = floor((n+1)*(2*n^2 + n + 24)/42).
a(n) = ceiling((2*n^3 + 3*n^2 + 25*n)/42).
a(n) = a(n-7) + (n+1)*(n-7) + 24, n > 6.
G.f.: x*(1+x)*(x^2 - x + 1)*(x^4 - x^3 + x^2 - x + 1) / ( (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^4 ).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-7) - 3*a(n-8) + 3*a(n-9) - a(n-10). (End)
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EXAMPLE
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a(7) = 0 + 1 + 1 + 2 + 3 + 4 + 6 + 7 = 24.
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MAPLE
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seq(round((2*n+1)*(n^2+n+12)/42), n=0..50)
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MATHEMATICA
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Ceiling[Range[0, 50]^2/7]//Accumulate (* Harvey P. Dale, Apr 12 2018 *)
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PROG
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(Magma) [&+[Ceiling(k^2/7): k in [0..n]]: n in [0..50]]; // Bruno Berselli, Apr 26 2011
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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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