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A132753 a(n) = 2^(n+1) - n + 1. 4
3, 4, 7, 14, 29, 60, 123, 250, 505, 1016, 2039, 4086, 8181, 16372, 32755, 65522, 131057, 262128, 524271, 1048558, 2097133, 4194284, 8388587, 16777194, 33554409, 67108840, 134217703, 268435430, 536870885, 1073741796, 2147483619 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Apart from a(0): Row sums of triangle A132752 (old name).
Apart from a(0): Binomial transform of [1, 3, 0, 4, 0, 4, 0, 4, ...].
LINKS
FORMULA
From Colin Barker, Mar 14 2014: (Start)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
G.f.: (3 - 8*x + 6*x^2)/((1-x)^2 * (1-2*x)). (End)
E.g.f.: (1-x)*exp(x) + 2*exp(2*x). - G. C. Greubel, Feb 16 2021
EXAMPLE
a(3) = 14 = sum of row 3 terms of triangle A132752: (3 + 5 + 5 + 1).
a(3) = 14 = (1, 3, 3, 1) dot (1, 3, 0, 4) = (1 + 9 + 0 + 4).
MAPLE
A132753:= n-> 2^(n+1) -n+1; seq(A132753(n), n=0..40) # G. C. Greubel, Feb 16 2021
MATHEMATICA
Table[2^(n+1) -n+1, {n, 0, 30}] (* Bruno Berselli, Aug 31 2013 *)
PROG
(PARI) a(n)=2^(n+1)-n+1
(PARI) Vec( (3-8*x+6*x^2)/((1-x)^2*(1-2*x)) + O(x^40)) \\ Colin Barker, Mar 14 2014
(Sage) [2^(n+1) -n+1 for n in (0..40)] # G. C. Greubel, Feb 16 2021
(Magma) [2^(n+1) -n+1: n in [0..40]]; // G. C. Greubel, Feb 16 2021
CROSSREFS
Cf. A132752.
Sequence in context: A095063 A003242 A073728 * A132407 A070035 A219277
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 28 2007
EXTENSIONS
More terms Vladimir Joseph Stephan Orlovsky, Dec 25 2008
Changed first member, and better name from Ralf Stephan, Aug 31 2013
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)