A249097
Ordered union of the sets {h^6, h >=1} and {3*k^6, k >=1}.
Original entry on oeis.org
1, 3, 64, 192, 729, 2187, 4096, 12288, 15625, 46656, 46875, 117649, 139968, 262144, 352947, 531441, 786432, 1000000, 1594323, 1771561, 2985984, 3000000, 4826809, 5314683, 7529536, 8957952, 11390625, 14480427, 16777216, 22588608, 24137569, 34012224, 34171875
Offset: 1
{h^6, h >=1} = {1, 64, 729, 4096, 15625, 46656, 117649, ...};
{3*k^6, k >=1} = {3, 192, 2187, 12288, 46875, 139968, ...};
so the union is {1, 3, 64, 192, 729, 2187, 4096, 12288, ...}
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upto(n)=setunion(apply(k->k^6, [1..sqrtnint(n,6)]), apply(k->3*k^6, [1..sqrtnint(n\3,6)])) \\ Andrew Howroyd, Feb 18 2025
A256278
a(0)=1, a(1)=2, a(n) = 31*a(n-1) - 29*a(n-2).
Original entry on oeis.org
1, 2, 33, 965, 28958, 869713, 26121321, 784539274, 23563199185, 707707535789, 21255600833094, 638400107288033, 19173990901769297, 575880114843495250, 17296237823997043137, 519482849213446974997, 15602377428720941973934, 468608697663159238917041
Offset: 0
For n=3, 31*a(2)-29*a(1) = 31*(33)-29*(2) = 1023-58 = 965.
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I:=[1,2]; [n le 2 select I[n] else 31*Self(n-1)-29*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 03 2015
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a:= n-> (<<0|1>, <-29|31>>^n. <<1, 2>>)[1,1]:
seq(a(n), n=0..23); # Alois P. Heinz, Dec 22 2023
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LinearRecurrence[{31, -29}, {1, 2}, 50] (* or *) CoefficientList[Series[(1 - 29 x)/(29 x^2 - 31 x + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 03 2015 *)
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print(1, end=', ')
print(2, end=', ')
an = [1,2]
for n in range(2,26):
print(31*an[n-1]-29*an[n-2], end=', ')
an.append(31*an[n-1]-29*an[n-2])
Showing 1-2 of 2 results.
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