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A123203
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A007318 * [1, 1, 4, 4, 4,...].
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8
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1, 2, 7, 20, 49, 110, 235, 488, 997, 2018, 4063, 8156, 16345, 32726, 65491, 131024, 262093, 524234, 1048519, 2097092, 4194241, 8388542, 16777147, 33554360, 67108789, 134217650, 268435375, 536870828, 1073741737, 2147483558
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OFFSET
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1,2
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COMMENTS
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An elephant sequence, see A175654. For the corner squares just one A[5] vector, with decimal value 186, leads to this sequence. For the central square this vector leads to the companion sequence A036563. - Johannes W. Meijer, Aug 15 2010
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REFERENCES
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Tamas Lengyel, On p-adic properties of the Stirling numbers of the first kind, Journal of Number Theory, 148 (2015) 73-94.
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LINKS
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Table of n, a(n) for n=1..30.
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
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FORMULA
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Binomial transform of [1, 1, 4, 4, 4,...] Row sums of triangle A131061.
From Johannes W. Meijer, Aug 15 2010: (Start)
a(n) = 2^(1+n) - 3*n.
a(n) = 3*A000295(n-1) + A000079(n-1).
(End)
G.f.: x*(1 - 2*x + 4*x^2)/((1-x)^2*(1-2*x)). - Colin Barker, Jul 28 2012
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Colin Barker, Jul 29 2012
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EXAMPLE
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a(4) = 20, row sums of 4th row of triangle A131062: (1, 9, 9, 1).
a(4) = 20 = (1, 3, 3, 1) dot (1, 1, 4, 4) = (1 + 3 + 12 + 4).
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MATHEMATICA
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s=1; lst={s}; Do[s+=(s+=n)+n++; AppendTo[lst, s], {n, 0, 5!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)
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CROSSREFS
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Cf. A109128, A131060, A131061, A131063, A131064, A131065, A131066.
Sequence in context: A090145 A244307 A270109 * A309298 A335927 A261054
Adjacent sequences: A123200 A123201 A123202 * A123204 A123205 A123206
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KEYWORD
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nonn,easy
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AUTHOR
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Gary W. Adamson, Jun 13 2007
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EXTENSIONS
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More terms from Vladimir Joseph Stephan Orlovsky, Nov 15 2008
The two given formulas corrected by Colin Barker, Jul 28 2012
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STATUS
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approved
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