A381476
Triangle read by rows: T(n,k) is the number of subsets of {1..n} with k elements such that every pair of distinct elements has a different difference, 0 <= k <= A143824(n).
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 4, 6, 2, 1, 5, 10, 6, 1, 6, 15, 14, 1, 7, 21, 26, 2, 1, 8, 28, 44, 10, 1, 9, 36, 68, 26, 1, 10, 45, 100, 60, 1, 11, 55, 140, 110, 1, 12, 66, 190, 190, 4, 1, 13, 78, 250, 304, 22, 1, 14, 91, 322, 466, 68, 1, 15, 105, 406, 676, 156
Offset: 0
Triangle begins:
0 | 1;
1 | 1, 1;
2 | 1, 2, 1;
3 | 1, 3, 3;
4 | 1, 4, 6, 2;
5 | 1, 5, 10, 6;
6 | 1, 6, 15, 14;
7 | 1, 7, 21, 26, 2;
8 | 1, 8, 28, 44, 10;
9 | 1, 9, 36, 68, 26;
10 | 1, 10, 45, 100, 60;
11 | 1, 11, 55, 140, 110;
12 | 1, 12, 66, 190, 190, 4;
...
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row(n)={
local(L=List());
my(recurse(k,r,b,w)=
if(k > n, if(r>=#L,listput(L,0)); L[1+r]++,
self()(k+1, r, b, w);
b+=1<
A377419
Minimum sum of a maximal subset of {1..n} such that every pair of distinct elements has a different difference.
Original entry on oeis.org
0, 1, 3, 3, 5, 7, 7, 7, 10, 10, 13, 15, 15, 15, 17, 17, 19, 19, 23, 24, 28, 29, 30, 30, 33, 34, 35, 36, 41, 41, 46, 48, 50, 52, 52, 53, 56, 56, 59, 59, 61, 63, 65, 68, 71, 71, 75, 81, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 95, 95, 98, 98, 98, 105, 112, 118, 121, 121, 124
Offset: 0
a(0) = 0 = sum of {}.
a(1) = 1 = sum of {1}.
a(2) = 3 = sum of {1,2}.
a(3) = 3 = sum of {1,2}.
a(4) = 5 = sum of {2,3}.
a(5) = 7 = sum of {1,2,4}.
a(12) = 15 = sum of {1,2,5,7} or {1,2,4,8}.
a(20) = 28 = sum of {2,5,10,11} or {1,2,4,8,13}.
See also the examples in A325879.
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a(n)={
my(ismaxl(b,w)=for(k=1, n, if(!bittest(b,k) && !bitand(w,bitor(b,1< n, if(ismaxl(b,w),0,n^2),
my(s=self()(k+1, b,w));
b+=1<
A382395
Number of maximum sized subsets of {1..n} such that every pair of distinct elements has a different difference.
Original entry on oeis.org
1, 1, 1, 3, 2, 6, 14, 2, 10, 26, 60, 110, 4, 22, 68, 156, 320, 584, 8, 24, 80, 206, 504, 1004, 1910, 3380, 10, 34, 98, 282, 760, 1618, 3334, 6360, 11482, 2, 22, 70, 214, 540, 1250, 2718, 5712, 10910, 20418, 2, 12, 30, 90, 230, 562, 1228, 2690, 5550, 11260, 21164, 2, 4, 6, 10, 18
Offset: 0
The a(0) = 1 set is {}.
The a(1) = 1 set is {1}.
The a(2) = 1 set is {1,2}.
The a(3) = 3 sets: {1,2}, {1,3}, {2,3}.
The a(4) = 2 sets: {1,2,4}, {1,3,4}.
The a(5) = 6 sets: {1,2,4}, {1,2,5}, {1,3,4}, {1,4,5}, {2,3,5}, {2,4,5}.
The a(6) = 14 sets: {1,2,4}, {1,2,5}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,5}, {1,4,6}, {1,5,6}, {2,3,5}, {2,3,6}, {2,4,5}, {2,5,6}, {3,4,6}, {3,5,6}.
The a(7) = 2 sets: {1,2,5,7}, {1,3,6,7}.
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a(n)={
local(best,count);
my(recurse(k,r,b,w)=
if(k > n, if(r>=best, if(r>best,best=r;count=0); count++),
self()(k+1, r, b, w);
b+=1<
A382396
Number of minimum sized maximal subsets of {1..n} such that every pair of distinct elements has a different difference.
Original entry on oeis.org
1, 1, 1, 3, 1, 6, 14, 18, 14, 10, 4, 110, 172, 216, 226, 214, 184, 152, 116, 82, 50, 26, 10, 3696, 3904, 3942, 3768, 3504, 3016, 2548, 2060, 1598, 1170, 832, 538, 330, 196, 106, 52, 20, 10, 4, 2, 69610, 62594, 55294, 47610, 40502, 33538, 27254, 21544, 16764, 12676, 9258, 6534, 4516, 3042, 1990, 1254, 754, 448
Offset: 0
The a(0) = 1 set is {}.
The a(1) = 1 set is {1}.
The a(2) = 1 set is {1,2}.
The a(3) = 3 sets: {1,2}, {1,3}, {2,3}.
The a(11) = 4 sets: {1,2,4,8}, {1,2,4,9}, {1,2,4,10}, {1,2,4,11}.
The a(42) = 2 sets: {10,18,19,25,30}, {13,18,24,25,33}.
See also the examples in A325879.
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a(n)={
local(best,count); best=n+1;
my(ismaxl(b,w)=for(k=1, n, if(!bittest(b,k) && !bitand(w,bitor(b,1< n, if(ismaxl(b,w),if(r
A382397
Minimum size of a maximal subset of {1..n} such that every pair of distinct elements has a different difference.
Original entry on oeis.org
0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 0
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a(n)={
my(ismaxl(b,w)=for(k=1, n, if(!bittest(b,k) && !bitand(w,bitor(b,1< n, if(ismaxl(b,w),0,n+1),
my(s=self()(k+1, b,w));
b+=1<
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