Original entry on oeis.org
2, 13, 28, 49, 74, 105, 140, 181, 226, 277, 332, 393, 458, 529, 604, 685, 770, 861, 956, 1057, 1162, 1273, 1388, 1509, 1634, 1765, 1900, 2041, 2186, 2337, 2492, 2653, 2818, 2989, 3164, 3345, 3530, 3721, 3916, 4117, 4322, 4533, 4748, 4969, 5194, 5425, 5660, 5901, 6146, 6397, 6652, 6913, 7178, 7449, 7724, 8005, 8290, 8581, 8876, 9177
Offset: 1
A358297
Bisection of main diagonal of A115009.
Original entry on oeis.org
6, 86, 418, 1282, 3106, 6394, 11822, 20074, 32086, 48934, 71554, 101250, 139350, 187254, 246690, 319346, 407302, 511714, 634726, 779074, 946622, 1140238, 1362082, 1614994, 1901930, 2224654, 2587402, 2992414, 3441754, 3941074, 4493414, 5102618, 5770646, 6501286, 7300578, 8170130, 9117486, 10145578, 11256062, 12454678, 13746910, 15140014, 16634530
Offset: 1
- D. M. Acketa, J. D. Zunic: On the number of linear partitions of the (m,n)-grid. Inform. Process. Lett., 38 (3) (1991), 163-168. See Table A.1.
- Jovisa Zunic, Note on the number of two-dimensional threshold functions, SIAM J. Discrete Math. Vol. 25 (2011), No. 3, pp. 1266-1268. See Equation (1.2).
A332351
Triangle read by rows: T(m,n) = Sum_{-m= n >= 1.
Original entry on oeis.org
0, 1, 6, 2, 13, 28, 3, 22, 49, 86, 4, 33, 74, 131, 200, 5, 46, 105, 188, 289, 418, 6, 61, 140, 251, 386, 559, 748, 7, 78, 181, 326, 503, 730, 979, 1282, 8, 97, 226, 409, 632, 919, 1234, 1617, 2040, 9, 118, 277, 502, 777, 1132, 1521, 1994, 2517, 3106, 10, 141, 332, 603, 934, 1361, 1828, 2397, 3026, 3735, 4492
Offset: 1
Triangle begins:
0,
1, 6,
2, 13, 28,
3, 22, 49, 86,
4, 33, 74, 131, 200,
5, 46, 105, 188, 289, 418,
6, 61, 140, 251, 386, 559, 748,
7, 78, 181, 326, 503, 730, 979, 1282,
8, 97, 226, 409, 632, 919, 1234, 1617, 2040,
9, 118, 277, 502, 777, 1132, 1521, 1994, 2517, 3106,
...
- Jovisa Zunic, Note on the number of two-dimensional threshold functions, SIAM J. Discrete Math. Vol. 25 (2011), No. 3, pp. 1266-1268. See Equation (1.2).
This is the lower triangle of the array in
A115009.
-
VR := proc(m,n,q) local a,i,j; a:=0;
for i from -m+1 to m-1 do for j from -n+1 to n-1 do
if gcd(i,j)=q then a:=a+(m-abs(i))*(n-abs(j)); fi; od: od: a; end;
for m from 1 to 12 do lprint(seq(VR(m,n,1)/2,n=1..m),); od:
-
A332351[m_,n_]:=Sum[If[CoprimeQ[i,j],2(m-i)(n-j),0],{i,m-1},{j,n-1}]+2m*n-m-n;Table[A332351[m,n],{m,15},{n,m}] (* Paolo Xausa, Oct 18 2023 *)
A115011
Array read by antidiagonals: let V(m,n) = Sum_{i=1..m, j=1..n, gcd(i,j)=1} (m+1-i)*(n+1-j), then T(m,n) = 2*(2*m*n+m+n+2*V(m,n)), for m >= 0, n >= 0.
Original entry on oeis.org
0, 2, 2, 4, 12, 4, 6, 26, 26, 6, 8, 44, 56, 44, 8, 10, 66, 98, 98, 66, 10, 12, 92, 148, 172, 148, 92, 12, 14, 122, 210, 262, 262, 210, 122, 14, 16, 156, 280, 376, 400, 376, 280, 156, 16, 18, 194, 362, 502, 578, 578, 502, 362, 194, 18, 20, 236, 452, 652, 772, 836, 772, 652, 452, 236, 20
Offset: 0
Twice
A115009, which see for further information.
-
V[m_, n_] := Sum[If[GCD[i, j] == 1, (m-i+1)(n-j+1), 0], {i, m}, {j, n}];
T[m_, n_] := 2(2m n + m + n + 2 V[m, n]);
Table[T[m-n, n], {m, 0, 10}, {n, 0, m}] // Flatten (* Jean-François Alcover, Oct 08 2018 *)
Showing 1-4 of 4 results.
Comments