A035253 Second differences are 2,2,1,2,1,1,2,1,1,1,2,1,1,1,1,2,1,1,1,1,1,2,.. (A035214).

4, 1, 0, 1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, 98, 114, 131, 150, 170, 191, 213, 236, 260, 286, 313, 341, 370, 400, 431, 463, 497, 532, 568, 605, 643, 682, 722, 763, 806, 850, 895, 941, 988, 1036, 1085, 1135, 1186, 1239, 1293, 1348, 1404, 1461, 1519, 1578

Offset: 0

Author

Robet Bronson (bob(AT)bronsons.com)

Keywords

• nonn
• easy

Crossrefs

Different from A005228. Cf. A035254, A060432.

Programs

Python

from math import isqrt
def A035253(n): return (k:=(r:=isqrt(m:=n<<1))+int((m<<2)>(r<<2)*(r+1)+1)-1)*(k*(-k-3)+6*n-8)//6+(n*(n-5)>>1)+3 # Chai Wah Wu, Jun 07 2025

Formula

a(n) = A060432(n-1)+4+n*(n-7)/2. - Chai Wah Wu, Jun 07 2025

Extensions

More terms from Chai Wah Wu, Jun 07 2025