A175822 Partial sums of ceiling(n^2/7).

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

Offset: 0

Author

Mircea Merca, Dec 05 2010

Keywords

• nonn
• easy

Comments

Partial sums of A036405.

Examples

			a(7) = 0 + 1 + 1 + 2 + 3 + 4 + 6 + 7 = 24.
		

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,-3,1,0,0,0,1,-3,3,-1).

Crossrefs

Cf. A036405.

Programs

Magma

[&+[Ceiling(k^2/7): k in [0..n]]: n in [0..50]];  // Bruno Berselli, Apr 26 2011

Maple

seq(round((2*n+1)*(n^2+n+12)/42),n=0..50)

Mathematica

Ceiling[Range[0,50]^2/7]//Accumulate (* Harvey P. Dale, Apr 12 2018 *)

PARI

a(n)=(n+1)*(2*n^2+n+24)\42 \\ Charles R Greathouse IV, Oct 16 2015

Formula

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.

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

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)