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

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

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

Example

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

Maple

seq(2+2^(1+n)-3*n, n=0..100); # Robert Israel, Nov 23 2014

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 *)

Prog

(Magma) [4] cat [n le 1 select 3 else Self(n-1)+2^n-3: n in [1..32]];
(Magma) [2+2^(1+n)-3*n: n in [0..32]]; // 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

Crossrefs

Cf. A094177, which may be an erroneous version of this sequence.

Sequence in context: A118701 A073254 A094177 * A244954 A353830 A060374

Adjacent sequences: A249450 A249451 A249452 * A249454 A249455 A249456

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Oct 29 2014

Status

approved