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A084174
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a(n) = +3*a(n-1) -1*a(n-2) -3*a(n-3) +2*a(n-4).
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5
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1, 1, 3, 6, 14, 29, 61, 124, 252, 507, 1019, 2042, 4090, 8185, 16377, 32760, 65528, 131063, 262135, 524278, 1048566, 2097141, 4194293, 8388596, 16777204, 33554419, 67108851, 134217714, 268435442, 536870897, 1073741809, 2147483632
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Original name was: Generalized Jacobsthal numbers.
Row sums of triangle A131087. - Gary W. Adamson, Jun 14 2007
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = 2^n+(-1)^n/4-(2*n+1)/4.
a(n+2) = a(n+1)+2*a(n)+n, a(0)=1, a(1)=1.
a(n) = A084172(n)-A001045(n).
a(n) = floor(2^n-n(n+1)/2). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007
G.f.: (1-2*x+x^2+x^3)/(1-3*x+x^2+3*x^3-2*x^4). [Colin Barker, Jan 16 2012]
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MAPLE
| seq(floor(2^n-n(n+1)/2), n=0..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007
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PROG
| (MAGMA) [2^n+(-1)^n/4-(2*n+1)/4: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
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CROSSREFS
| Cf. A131087.
Sequence in context: A055890 A038359 A038360 * A036658 A077067 A083797
Adjacent sequences: A084171 A084172 A084173 * A084175 A084176 A084177
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 18 2003
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