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A175161
a(n) = 8*(2^n + 1).
7
16, 24, 40, 72, 136, 264, 520, 1032, 2056, 4104, 8200, 16392, 32776, 65544, 131080, 262152, 524296, 1048584, 2097160, 4194312, 8388616, 16777224, 33554440, 67108872, 134217736, 268435464, 536870920, 1073741832, 2147483656, 4294967304, 8589934600, 17179869192
OFFSET
0,1
FORMULA
a(n) = A173786(n+3, 3).
a(n) = A175166(2*n)/A159741(n) for n > 0.
a(n) = 3*a(n-1) -2*a(n-2) with a(0)=16, a(1)=24. - Vincenzo Librandi, Dec 28 2010
G.f.: 8*(2 - 3*x)/((1-x)*(1-2*x)). - Chai Wah Wu, Jun 20 2020
a(n) = 8 * A000051(n). - Alois P. Heinz, Jun 20 2020
E.g.f.: 8*(exp(2*x) + exp(x)). - G. C. Greubel, Jul 08 2021
MATHEMATICA
8*(2^Range[0, 40] + 1) (* G. C. Greubel, Jul 08 2021 *)
LinearRecurrence[{3, -2}, {16, 24}, 40] (* Harvey P. Dale, Feb 10 2022 *)
PROG
(Magma) I:=[16, 24]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021
(Sage) [8*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021
CROSSREFS
Sequences of the form m*(2^n + 1): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), this sequence (m=8), A175162 (m=16), A175163 (m=32).
Sequence in context: A120142 A110228 A269519 * A045875 A046434 A111046
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Feb 28 2010
STATUS
approved