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Search: id:A084175
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| 0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575, 244335800775, 977343902151, 3909374210503, 15637499638215, 62549992960455
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OFFSET
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0,3
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COMMENT
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a(n)=A001045(n)*A001045(n+1). Inverse binomial transform is A001019 doubled up. Binomial transform is A084177. Partial sums of A003683.
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FORMULA
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a(n)=(2*4^n-(-2)^n-1)/9; a(n)=3a(n-1)+6a(n-2)-8a(n-3), a(0)=0, a(1)=1, a(2)=3; G.f.:x/((1+2x)(1-x)(1-4x)); E.g.f.: (2*exp(4x)-exp(x)-exp(-2x))/9.
a(n+1)-4a(n)= 1, -1, 3, -5, 11, ... = A001045(n+1) signed. - Paul Curtz (bpcrtz(AT)free.fr), May 19 2008
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CROSSREFS
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Except for initial terms, same as A015249 and A084152.
Cf. A001654, A084158, A084159, A084152, A015249.
Adjacent sequences: A084172 A084173 A084174 this_sequence A084176 A084177 A084178
Sequence in context: A007973 A015249 A084152 this_sequence A081951 A033853 A049187
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 18 2003
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