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A175831
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Partial sums of ceiling(n^2/12).
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1
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0, 1, 2, 3, 5, 8, 11, 16, 22, 29, 38, 49, 61, 76, 93, 112, 134, 159, 186, 217, 251, 288, 329, 374, 422, 475, 532, 593, 659, 730, 805, 886, 972, 1063, 1160, 1263, 1371, 1486, 1607, 1734, 1868, 2009, 2156, 2311, 2473, 2642, 2819, 3004, 3196, 3397, 3606
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OFFSET
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0,3
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COMMENTS
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Partial sums of A036410.
There are several sequences of integers of the form ceiling(n^2/k) for whose partial sums we can establish identities as following (only for k = 2,...,8,10,11,12, 14,15,16,19,20,23,24).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (2,0,-1,-1,0,2,-1).
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)=round((2*n+1)*(2*n^2+2*n+41)/144).
a(n)=floor((n+1)*(2*n^2+n+41)/72).
a(n)=ceil((2*n^3+3*n^2+42*n)/72).
a(n)=a(n-12)+(n+1)*(n-12)+61.
G.f. x*(1-x^2+x^4) / ( (1+x)*(1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Jun 22 2011
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EXAMPLE
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a(12)=0+1+1+1+2+3+3+5+6+7+9+11+12
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MAPLE
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seq(floor((n+1)*(2*n^2+n+41)/72), n=0..50)
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PROG
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(MAGMA) [Round((2*n+1)*(2*n^2+2*n+41)/144): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011
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CROSSREFS
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Cf. A036410.
Sequence in context: A008762 A101018 A006336 * A070228 A173599 A006304
Adjacent sequences: A175828 A175829 A175830 * A175832 A175833 A175834
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KEYWORD
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nonn
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AUTHOR
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Mircea Merca, Dec 05 2010
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STATUS
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approved
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