A274401 - OEIS

%I #10 Aug 04 2024 18:07:33

%S 0,1,8,3,16,7,32,13,48,19,80,29,96,41,144,49,176,65,224,83,256,95,336,

%T 117,368,137,464,155,512,183,576,213,640,233,768,257,816,293,960,317,

%U 1024,357,1120,399,1200,423,1376,469,1440

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

%H D. M. Acketa, N. Divljak, J. Zunic. <a href="https://www.emis.de/journals/NSJOM/Papers/24_1/NSJOM_24_1_309_319.pdf">On balanced linear 4-partitions of the (n,n)-grid</a>. Novi Sad Journal of Mathematics 24:1 (1994), 309-319.

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

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

%o (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)) ); }

%o (Python)

%o # uses programs from A002088 and A049690

%o 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

%Y Cf. A002088, A049690, A099957.

%K nonn,easy

%O 1,3

%A _Max Alekseyev_, Jun 20 2016