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A091775
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a(n)=1+4^n+9^n+16^n.
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1
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30, 354, 4890, 72354, 1108650, 17312754, 273234810, 4338079554, 69107159370, 1102999460754, 17623571298330, 281757423024354, 4506141560307690, 72080471098818354, 1153127396812683450, 18448597098193370754, 295164582378232361610, 4722516577573661689554
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| n>0 a(n) = 5^(2*n+1)/(2*n+1)*sum(k=0, 2*n+1, (1/5)^k*C(2*n+1, k)*B(k)) where B(k) is the k-th Bernoulli number.
G.f.: 16/(1 - 16 x) + 9/(1 - 9 x) + 4/(1 - 4 x) + 1/(1 - x) [From Harvey P. Dale, May 04 2011]
a(0)=30, a(1)=354, a(2)=4890, a(3)=72354, a(n)=30a(n-1)-273a(n-2)+ 820a(n-3)-576a(n-4) [From Harvey P. Dale, May 04 2011]
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MATHEMATICA
| Table[1+4^n+9^n+16^n, {n, 20}] (* or *) LinearRecurrence[ {30, -273, 820, -576}, {30, 354, 4890, 72354}, 20](* From Harvey P. Dale, May 04 2011 *)
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CROSSREFS
| Cf. A052539, A074515.
Sequence in context: A115500 A125418 A107916 * A008656 A179717 A086864
Adjacent sequences: A091772 A091773 A091774 * A091776 A091777 A091778
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 06 2004
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EXTENSIONS
| Corrected and extended by Harvey P. Dale, May 04 2011.
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