A249453 a(0) = 4; for n>0, a(n) = a(n-1) + 2^n - 3.
4, 3, 4, 9, 22, 51, 112, 237, 490, 999, 2020, 4065, 8158, 16347, 32728, 65493, 131026, 262095, 524236, 1048521, 2097094, 4194243, 8388544, 16777149, 33554362, 67108791, 134217652, 268435377, 536870830, 1073741739, 2147483560, 4294967205, 8589934498
Offset: 0
Examples
Start with a(0)=4 and step = -1, then increase the step after each iteration by 2^n: 4-1 = 3; step+2 = 1; 3+1 = 4; step+4 = 5; 4+5 = 9; step+8 = 13; 9+13 = 22; step+16=29; 22+29 = 51; ... - _M. F. Hasler_, Oct 31 2014
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
Crossrefs
Cf. A094177, which may be an erroneous version of this sequence.
Programs
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Magma
[4] cat [n le 1 select 3 else Self(n-1)+2^n-3: n in [1..32]];
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Magma
[2+2^(1+n)-3*n: n in [0..32]]; // Vincenzo Librandi, Oct 31 2014
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Maple
seq(2+2^(1+n)-3*n, n=0..100); # Robert Israel, Nov 23 2014
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Mathematica
a249453[n_Integer] := Module[{a}, a[0] = 4; a[k_] := a[k - 1] + 2^k - 3; a /@ Range[0, n]]; a249453[32] (* Michael De Vlieger, Nov 23 2014 *) CoefficientList[Series[(12 x^2 - 13 x+4)/((1 - x)^2 (1 - 2 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 31 2014 *) -
PARI
Vec(-(12*x^2-13*x+4)/((x-1)^2*(2*x-1)) + O(x^100)) \\ Colin Barker, Oct 30 2014
Formula
a(n) = 2*a(n-1) + 3*n - 8.
a(n) = 3*a(n-1) - 2*a(n-2) + 3.
From Colin Barker, Oct 30 2014: (Start)
a(n) = 2+2^(1+n)-3*n.
G.f.: -(12*x^2-13*x+4) / ((x-1)^2*(2*x-1)).
(End)
E.g.f.: (2-3*x)*exp(x) + 2*exp(2*x). - Robert Israel, Nov 23 2014