A175826 Partial sums of ceiling(n^2/8).

0, 1, 2, 4, 6, 10, 15, 22, 30, 41, 54, 70, 88, 110, 135, 164, 196, 233, 274, 320, 370, 426, 487, 554, 626, 705, 790, 882, 980, 1086, 1199, 1320, 1448, 1585, 1730, 1884, 2046, 2218, 2399, 2590, 2790, 3001, 3222, 3454, 3696, 3950, 4215, 4492, 4780, 5081, 5394

Offset: 0

Author

Mircea Merca, Dec 05 2010

Keywords

• nonn
• easy

Comments

Partial sums of A036406.

Examples

			a(8) = 0 + 1 + 1 + 2 + 2 + 4 + 5 + 7 + 8 = 30.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..860
• 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,-3,1,1,-3,3,-1).

Crossrefs

Cf. A175822.

Programs

Magma

[&+[Ceiling(k^2/8): k in [0..n]]: n in [0..50]];  // Bruno Berselli, Apr 26 2011

Maple

seq(floor((n+1)*(2*n^2+n+27)/48),n=0..50)

PARI

a(n)=(n+1)*(2*n^2+n+27)\48 \\ Charles R Greathouse IV, Oct 19 2022

Formula

a(n) = round((2*n+1)*(2*n^2 + 2*n + 27)/96).

a(n) = floor((n+1)*(2*n^2 + n + 27)/48).

a(n) = ceiling((2*n^3 + 3*n^2 + 28*n)/48).

a(n) = a(n-8) + (n+1)*(n-8) + 30.

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

G.f.: x*(1 - x + x^2 + x^4 - x^3) / ( (1+x)*(1+x^2)*(x-1)^4 ).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7). (End)