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

1,3

Links

Table of n, a(n) for n=1..49.

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.

Formula

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

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

Prog

(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

Crossrefs

Cf. A002088, A049690, A099957.

Sequence in context: A070486 A195161 A144433 * A228691 A376082 A228313

Adjacent sequences: A274398 A274399 A274400 * A274402 A274403 A274404

Keyword

nonn,easy

Author

Max Alekseyev, Jun 20 2016

Status

approved