A171152 Partial sums of A118011.

3, 9, 17, 28, 41, 56, 74, 94, 116, 140, 167, 196, 227, 260, 295, 333, 373, 415, 459, 505, 553, 604, 657, 712, 769, 828, 889, 952, 1018, 1086, 1156, 1228, 1302, 1378, 1456, 1536, 1619, 1704, 1791, 1880, 1971, 2064, 2159, 2256, 2355, 2457, 2561, 2667, 2775, 2885, 2997, 3111

Offset: 1

Author

Gerald Hillier, Dec 04 2009

Keywords

• nonn

Examples

			a(1) = 3;
a(2) = 3+6 = 9;
a(3) = 3+6+8 = 17;
a(4) = 3+6+8+11 = 28.
		

Crossrefs

Cf. A118011 (complement of the Connell sequence).

Programs

PARI

vector(80, n, R = round(sqrt(2*n)); n^2+n+R*((6*n+1)-R^2)/6) \\ Michel Marcus, Apr 17 2015

Python

from math import isqrt
def A171152(n): return n*(n+1)+(r:=(m:=isqrt(k:=n<<1))+int((k-m*(m+1)<<2)>=1))*(3*k+1-r**2)//6 # Chai Wah Wu, Jul 30 2022

Formula

Set R = round(sqrt(2*n)), then a(n) = n^2+n+R*((6*n+1)-R^2)/6.

Extensions

More terms from Michel Marcus, Apr 17 2015