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Search: id:A084868
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| A084868 |
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Main diagonal of symmetric square table A084867, in which the antidiagonal sums (A006012) form the first row shifted left. |
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3
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| 1, 2, 8, 36, 168, 796, 3800, 18216, 87536, 421292, 2029592, 9784088, 47187536, 227651352, 1098523504, 5301727824, 25590307552, 123529362124, 596337248024, 2878947861432, 13899229883024, 67105641925064, 323993230750672
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The Hankel transform (see A001906 for definition) of this sequence is A000302 (powers of 4) : 1, 4, 16, 64, 256, 1024, ... - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 17 2005
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FORMULA
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Differential equation: (16*x^3+12*x^2-8x+1)*x*diff(A(x), x) + (8x^3-12*x^2+6*x-1)*A(x) + (8x^2-6*x+1) = 0.
G.f.: ((1-4x)+2x*sqrt(1-4x))/(1-4x-4x^2). a(n)(n-1)=a(n-1)(8n-14)-a(n-2)12(n-3)-a(n-3)8(2n-5), n>2. Invert transform of A028329(n-1). Hankel number wall zig-zag diagonal is A011782. - Michael Somos, Sep 14 2003
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PROGRAM
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(PARI) a(n)=polcoeff((1-4*x+2*x*sqrt(1-4*x+x*O(x^n)))/(1-4*x-4*x^2), n) (from Michael Somos)
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CROSSREFS
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Cf. A006012, A084867.
Sequence in context: A152124 A147722 A089387 this_sequence A109980 A110837 A166229
Adjacent sequences: A084865 A084866 A084867 this_sequence A084869 A084870 A084871
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 10 2003, Jun 11 2003
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