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Search: id:A106853
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| A106853 |
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Expansion of 1/(1-x(1-4x)). |
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+0
10
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| 1, 1, -3, -7, 5, 33, 13, -119, -171, 305, 989, -231, -4187, -3263, 13485, 26537, -27403, -133551, -23939, 510265, 606021, -1435039, -3859123, 1881033, 17317525, 9793393, -59476707, -98650279, 139256549, 533857665, -23168531, -2158599191, -2065925067, 6568471697, 14832171965
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums of Riordan array (1,x(1-4x)). In general, a(n)=sum{k=0..n,(-1)^(n-k)*binomial(k,n-k)*r^(n-k)} yields the row sums of the Riordan array (1,x(1-kx)).
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FORMULA
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G.f.:1/(1-x+4x^2); a(n)=2^n(cos(2n*atan(sqrt(15)/5))+sqrt(15)sin(2n*atan(sqrt(15)/5))/15); a(n)=((1+sqrt(-15))^(n+1)-(1-sqrt(-15))^(n+1))/(2^(n+1)sqrt(-15)); a(n)=sum{k=0..n, (-1)^(n-k)*binomial(k, n-k)*4^(n-k)}.
a(n)=a(n-1)-4*a(n-2), a(0)=1, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 21 2008]
a(n)=Sum_{k, 0<=k<=n}A109466(n,k)*4^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 25 2008]
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PROGRAM
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(Other) sage: [lucas_number1(n, 1, 4) for n in xrange(1, 36)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Sequence in context: A161818 A161509 A108974 this_sequence A083778 A107785 A001663
Adjacent sequences: A106850 A106851 A106852 this_sequence A106854 A106855 A106856
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 08 2005
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