A133095 Row sums of triangle A133094.

1, 4, 9, 20, 43, 90, 185, 376, 759, 1526, 3061, 6132, 12275, 24562, 49137, 98288, 196591, 393198, 786413, 1572844, 3145707, 6291434, 12582889, 25165800, 50331623, 100663270, 201326565, 402653156, 805306339, 1610612706, 3221225441, 6442450912, 12884901855, 25769803742, 51539607517

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

Binomial transform of [1, 3, 2, 4, 2, 4, 2, 4, ...].

From G. C. Greubel, Oct 21 2017: (Start)

a(n) = 3*2^(n-1) - n, for n >= 2.

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

G.f.: x*(1 - 2*x^2 + 2*x^3)/((1-2*x)*(1-x)^2).

E.g.f.: (3*exp(2*x) - 2*x*exp(x) - 2*x - 3)/2. (End)

a(n) = A123720(n) for n >= 2. - Georg Fischer, Nov 02 2018

Example

a(4) = 20 = sum of row 4 terms of triangle A133094: (7 + 7 + 5 + 1).
a(4) = 20 = (1, 3, 3, 1) dot (1, 3, 2, 4) = (1 + 9 + 6 + 4).

Mathematica

Join[{1}, Table[ 3*2^(n - 1) - n, {n, 2, 50}]] (* G. C. Greubel, Oct 21 2017 *)
LinearRecurrence[{4, -5, 2}, {1, 4, 9, 20}, 50] (* Harvey P. Dale, Aug 09 2022 *)

Prog

(PARI) concat(1, for(n=1, 50, print1(3*2^(n - 1) - n, ", "))) \\ G. C. Greubel, Oct 21 2017
(Magma) [1] cat [3*2^(n - 1) - n: n in [2..50]]; // G. C. Greubel, Oct 21 2017

Crossrefs

Cf. A123720, A133094.

Sequence in context: A051136 A156321 A276778 * A132175 A019493 A019492

Adjacent sequences: A133092 A133093 A133094 * A133096 A133097 A133098

Keyword

nonn

Author

Gary W. Adamson, Sep 09 2007

Extensions

Terms a(11) onward added by G. C. Greubel, Oct 21 2017

Status

approved