A173653 Partial sums of floor(n^2/10) (A056865)

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

Offset

0,6

Links

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.

Formula

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]

Example

a(9) = 0+0+0+0+1+2+3+4+6+8 = 24

Mathematica

Accumulate[Floor[Range[0, 50]^2/10]] (* Harvey P. Dale, May 31 2012 *)

Crossrefs

Cf. A056865

Sequence in context: A066377 A259823 A264847 * A122046 A078663 A173691

Adjacent sequences: A173650 A173651 A173652 * A173654 A173655 A173656

Keyword

nonn

Author

Mircea Merca, Nov 24 2010

Status

approved