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A144472
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Negative values along the main diagonal of the array defined by A020806 and its differences.
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5
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-1, 2, 9, 13, 31, 57, 119, 233, 471, 937, 1879, 3753, 7511, 15017, 30039, 60073, 120151, 240297, 480599, 961193, 1922391, 3844777, 7689559, 15379113, 30758231, 61516457, 123032919, 246065833, 492131671, 984263337, 1968526679, 3937053353, 7874106711
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n+1) - 2*a(n) = (-1)^n*A010716(n), n>1, period 2.
G.f.: x*(1-3*x-9*x^2) / ((1+x)*(2*x-1)). - R. J. Mathar, Oct 24 2008
a(n) = 11*2^(n-2)/3 - 5*(-1)^n/3, n>1. - R. J. Mathar, Oct 24 2008
a(n) = (11*2^n - 20) / 12 for n>1 and even.
a(n) = (11*2^n + 20) / 12 for n>1 and odd.
a(n) = a(n-1) + 2*a(n-2) for n>3.
(End)
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EXAMPLE
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A020806 and its repeated differences in the next rows start as follows:
..1,..4,..2,..8,..5,..7,..1,..4,..2,..8, <- A020806
..3,.-2,..6,.-3,..2,.-6,..3,.-2,..6,.-3, <- A131969
.-5,..8,.-9,..5,.-8,..9,.-5,..8,.-9,..5,
.13,-17,.14,-13,.17,-14,.13,-17,.14,-13,
-30,.31,-27,.30,-31,.27,-30,.31,-27,.30,
.61,-58,.57,-61,.58,-57,.61,-58,.57,-61,
The diagonal is 1,-2,-9,-13,-31,... which yields a(n) after signs are flipped.
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MATHEMATICA
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PROG
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(PARI) Vec(-x*(1 - 3*x - 9*x^2) / ((1 + x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, Nov 06 2017
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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