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Search: id:A113250
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| A113250 |
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Corresponds to m = 4 in a family of 4th order linear recurrence sequences given by a(m,n) = m^4*a(n-4) + (2*m)^2*a(n-3) - 4*a(m-1), a(m,0) = -1, a(m,1) = 4, a(m,2) = -13 + 6*(m-1) + 3*(m-1)^2, a(m,3) = (-8+m^2)^2. |
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+0
8
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| -1, 4, 32, 64, -256, 4096, -4096, 16384, 131072, 262144, -1048576, 16777216, -16777216, 67108864, 536870912, 1073741824, -4294967296, 68719476736, -68719476736, 274877906944, 2199023255552, 4398046511104, -17592186044416, 281474976710656, -281474976710656
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OFFSET
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0,2
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COMMENT
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Conjecture: a(m, 2*n+1) is a perfect square for all m (see A113249), Initial terms factored (without regards to sign): 1, 4, (2)^5, (2)^6,(2)^8, (2)^12, (2)^12, (2)^14, (2)^17, (2)^18, (2)^20, (2)^24, (2)^24, (2)^26, (2)^29, (2)^30, (2)^32, (2)^36
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FORMULA
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G.f. (48*x^2-1+256*x^3)/((4*x+1)*(4*x-1)*(16*x^2+4*x+1))
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CROSSREFS
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Cf. A000302, A097948, A056450, A113249, A113251, A113252, A113253, A113254, A113255, A113256.
Sequence in context: A078092 A076137 A138340 this_sequence A012036 A153794 A108914
Adjacent sequences: A113247 A113248 A113249 this_sequence A113251 A113252 A113253
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KEYWORD
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easy,sign
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 18 2005
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