login
A171152
Partial sums of A118011.
2
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
1,1
FORMULA
Set R = round(sqrt(2*n)), then a(n) = n^2+n+R*((6*n+1)-R^2)/6.
EXAMPLE
a(1) = 3;
a(2) = 3+6 = 9;
a(3) = 3+6+8 = 17;
a(4) = 3+6+8+11 = 28.
PROG
(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
CROSSREFS
Cf. A118011 (complement of the Connell sequence).
Sequence in context: A202253 A057258 A018466 * A035107 A090262 A190815
KEYWORD
nonn
AUTHOR
Gerald Hillier, Dec 04 2009
EXTENSIONS
More terms from Michel Marcus, Apr 17 2015
STATUS
approved