A175827 Partial sums of ceiling(n^2/10).

0, 1, 2, 3, 5, 8, 12, 17, 24, 33, 43, 56, 71, 88, 108, 131, 157, 186, 219, 256, 296, 341, 390, 443, 501, 564, 632, 705, 784, 869, 959, 1056, 1159, 1268, 1384, 1507, 1637, 1774, 1919, 2072, 2232, 2401, 2578, 2763, 2957, 3160, 3372, 3593, 3824, 4065, 4315, 4576, 4847, 5128, 5420

Offset

0,3

Comments

Partial sums of A036408.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,1,-3,3,-1).

Formula

a(n) = round((2*n+1)*(2*n^2 + 2*n + 27)/120).

a(n) = floor((2*n^3 + 3*n^2 + 28*n + 36)/60).

a(n) = ceiling((2*n^3 + 3*n^2 + 28*n - 9)/60).

a(n) = a(n-10) + (n+1)*(n-10) + 43.

From R. J. Mathar, Dec 06 2010: (Start)

G.f.: x*(1 - x + x^3 + x^7 - x^9 + x^10) / ( (1+x)*(x^4 + x^3 + x^2 + x + 1)*(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-10) - 3*a(n-11) + 3*a(n-12) - a(n-13). (End)

Example

a(10) = 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 7 + 9 + 10 = 43.

Maple

seq(ceil((2*n^3+3*n^2+28*n-9)/60), n=0..50);

Mathematica

A175827[n_] := Quotient[n*(n*(2*n + 3) + 28) + 36, 60]; Array[A175827, 60, 0] (* or *)
Accumulate[Ceiling[Range[0, 59]^2/10]] (* Paolo Xausa, Apr 01 2026 *)

Prog

(Magma) [Round((2*n+1)*(2*n^2+2*n+27)/120): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011

Crossrefs

Cf. A175822, A175826.

Sequence in context: A275580 A175829 A241552 * A061535 A280276 A233969

Adjacent sequences: A175824 A175825 A175826 * A175828 A175829 A175830

Keyword

nonn,easy

Author

Mircea Merca, Dec 05 2010

Status

approved