A092795
Number of connected relations.
Original entry on oeis.org
1, 67, 1993, 43891, 836521, 14764627, 249723433, 4123297651, 67157947561, 1085384064787, 17464790421673, 280328391247411, 4493290901135401, 71964955947764947, 1152089156508284713, 18439265231953981171, 295080697103288816041, 4721762414918959913107
Offset: 1
- G. C. Greubel, Table of n, a(n) for n = 1..825
- G. Kilibarda and V. Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
- Index entries for linear recurrences with constant coefficients, signature (43,-701,5477,-20658,30240).
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[16^n - 4*9^n - 3*7^n + 12*6^n - 6*5^n: n in [1..50]]; // G. C. Greubel, Oct 08 2017
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Table[16^n - 4*9^n - 3*7^n + 12*6^n - 6*5^n, {n, 1, 50}] (* G. C. Greubel, Oct 08 2017 *)
LinearRecurrence[{43,-701,5477,-20658,30240},{1,67,1993,43891,836521},20] (* Harvey P. Dale, May 24 2025 *)
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for(n=1,50, print1(16^n - 4*9^n - 3*7^n + 12*6^n - 6*5^n, ", ")) \\ G. C. Greubel, Oct 08 2017
A092796
Number of connected relations.
Original entry on oeis.org
1, 213, 14857, 694485, 27005881, 957263493, 32333393737, 1064686990965, 34589700409561, 1115777278022373, 35856732186282217, 1149998292486777045, 36843831022923582841, 1179748027215029366853, 37764598757179830172297, 1208682260675932309564725
Offset: 1
- G. C. Greubel, Table of n, a(n) for n = 1..660
- G. Kilibarda and V. Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
- Index entries for linear recurrences with constant coefficients, signature (91,-3299,62713,-682172,4276972,-14386144,20106240).
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[32^n - 5*17^n - 10*11^n + 20*10^n + 30*8^n - 60*7^n + 24*6^n: n in [0..50]]; // G. C. Greubel, Oct 08 2017
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Table[32^n - 5*17^n - 10*11^n + 20*10^n + 30*8^n - 60*7^n + 24*6^n, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
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for(n=0,50, print1(32^n - 5*17^n - 10*11^n + 20*10^n + 30*8^n - 60*7^n + 24*6^n, ", ")) \\ G. C. Greubel, Oct 08 2017
A092797
Number of connected relations.
Original entry on oeis.org
1, 667, 108817, 10796275, 858251401, 61283936827, 4147211888737, 273109341611395, 17736960725057401, 1143745441025278987, 73483870162431314257, 4712360023676936085715, 301901195708380781658601, 19331914197940256185117147, 1237580377249840094294765377
Offset: 1
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[64^n - 6*33^n - 15*19^n + 30*18^n - 10*15^n + 120*12^n - 120*11^n + 30*10^n - 270*9^n + 360*8^n - 120*7^n: n in [0..50]]; // G. C. Greubel, Oct 08 2017
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Table[64^n - 6*33^n - 15*19^n + 30*18^n - 10*15^n + 120*12^n - 120*11^n + 30*10^n - 270*9^n + 360*8^n - 120*7^n, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
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for(n=0,50, print1(64^n - 6*33^n - 15*19^n + 30*18^n - 10*15^n + 120*12^n - 120*11^n + 30*10^n - 270*9^n + 360*8^n - 120*7^n, ", ")) \\ G. C. Greubel, Oct 08 2017
A255192
Triangle of number of connected subgraphs of K(n,n) with m edges.
Original entry on oeis.org
1, 4, 1, 81, 78, 36, 9, 1, 4096, 8424, 9552, 7464, 4272, 1812, 560, 120, 16, 1, 390625, 1359640, 2696200, 3880300, 4394600, 4059000, 3111140, 1994150, 1070150, 478800, 176900, 53120, 12650, 2300, 300, 25, 1, 60466176, 314452800, 939988800, 2075760000
Offset: 1
Triangle begins:
----|------------------------------------------------------------
n\m | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
----|------------------------------------------------------------
1 | 1
2 | - - 4 1
3 | - - - - 81 78 36 9 1
4 | - - - - - - 4096 8424 9552 7464 4272 1812 560 120 16 1
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from math import comb as binomial
def f(x, a, b, k):
if b == k == 0:
return 1
if b == 0 or k == 0:
return 0
if x == a:
return sum(binomial(a, n) * f(x, x, b - 1, k - n) for n in range(1, a + 1))
return sum(binomial(b, n) * f(x, x, n, k2) * f(n, b, a - x, k - k2)
for n in range(1, b + 1) for k2 in range(0, k + 1) )
def a(n, m):
return f(1, n, n, m)
for n in range(1, 5):
print([a(n, m) for m in range(1, n * n + 1)])
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