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A173653
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Partial sums of floor(n^2/10) (A056865)
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0
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0, 0, 0, 0, 1, 3, 6, 10, 16, 24, 34, 46, 60, 76, 95, 117, 142, 170, 202, 238, 278, 322, 370, 422, 479, 541, 608, 680, 758, 842, 932, 1028, 1130, 1238, 1353, 1475, 1604, 1740, 1884, 2036, 2196, 2364, 2540, 2724, 2917, 3119, 3330, 3550, 3780
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OFFSET
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0,6
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LINKS
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Table of n, a(n) for n=0..48.
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
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FORMULA
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a(n) = sum(k=0..n,floor(k^2/10)).
a(n) = a(n-10)+(n-5)^2+n-1 , n>9.
G.f.: x^4*(1+x^4) / ( (1+x)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^4 ). [R. J. Mathar, Nov 24 2010]
a(n)= +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-10) -3*a(n-11) +3*a(n-12) -a(n-13). [R. J. Mathar, Nov 24 2010]
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EXAMPLE
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a(9) = 0+0+0+0+1+2+3+4+6+8 = 24
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MATHEMATICA
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Accumulate[Floor[Range[0, 50]^2/10]] (* Harvey P. Dale, May 31 2012 *)
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CROSSREFS
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Cf. A056865
Sequence in context: A121776 A088637 A066377 * A122046 A078663 A173691
Adjacent sequences: A173650 A173651 A173652 * A173654 A173655 A173656
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KEYWORD
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nonn
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AUTHOR
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Mircea Merca, Nov 24 2010
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STATUS
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approved
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