A274401 Number of balanced linear 4-partitions of the n X n grid.

0, 1, 8, 3, 16, 7, 32, 13, 48, 19, 80, 29, 96, 41, 144, 49, 176, 65, 224, 83, 256, 95, 336, 117, 368, 137, 464, 155, 512, 183, 576, 213, 640, 233, 768, 257, 816, 293, 960, 317, 1024, 357, 1120, 399, 1200, 423, 1376, 469, 1440

Offset: 1

Author

Max Alekseyev, Jun 20 2016

Keywords

• nonn
• easy

Links

• D. M. Acketa, N. Divljak, J. Zunic. On balanced linear 4-partitions of the (n,n)-grid. Novi Sad Journal of Mathematics 24:1 (1994), 309-319.

Crossrefs

Cf. A002088, A049690, A099957.

Programs

PARI

{ a(n) = if(n%2, 8*sum(m=1,(n-1)\2,eulerphi(m)), sum(m=0,(n-1)\2,eulerphi(2*m+1)) ); }

Python

# uses programs from A002088 and A049690
def A274401(n): return (A002088(n>>1)<<3) if n&1 else A002088(n-1)-A049690((n>>1)-1) # Chai Wah Wu, Aug 04 2024

Formula

For odd n, a(n) = 8 * A002088((n-1)/2).

For even n, a(n) = A099957(n/2).