A132730 Row sums of triangle A132729.

1, 2, 3, 8, 21, 50, 111, 236, 489, 998, 2019, 4064, 8157, 16346, 32727, 65492, 131025, 262094, 524235, 1048520, 2097093, 4194242, 8388543, 16777148, 33554361, 67108790, 134217651, 268435376, 536870829

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

Binomial transform of [1, 1, 0, 4, 0, 4, 0, 4, ...].

a(n) = 2^(n+1) - 3*n + 1, for n > 0. - R. J. Mathar, Apr 04 2012

From G. C. Greubel, Feb 14 2021: (Start)

G.f.: (1 - 2*x + 4*x^3)/((1-x)^2 * (1-2*x)).

E.g.f.: -2 + (1-3*x)*exp(x) + 2*exp(2*x). (End)

Example

a(4) = 21 = sum of row 4 terms of triangle A132729: (1 + 5 + 9 + 5 + 1).
a(3) = 8 = (1, 3, 3, 1) dot (1, 1, 0, 4) = (1 + 3 + 0 + 4).

Mathematica

LinearRecurrence[{4, -5, 2}, {1, 2, 3, 8}, 30] (* Harvey P. Dale, Dec 30 2015 *)
Table[2^(n+1) -3*n +1 -2*Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Feb 14 2021 *)

Prog

(Sage) [1]+[2^(n+1) -3*n +1 for n in (1..30)] # G. C. Greubel, Feb 14 2021
(Magma) [1] cat [2^(n+1) -3*n +1: n in [0..30]]; // G. C. Greubel, Feb 14 2021

Crossrefs

Cf. A132729.

Sequence in context: A251608 A288252 A122263 * A004790 A245464 A243562

Adjacent sequences: A132727 A132728 A132729 * A132731 A132732 A132733

Keyword

nonn,easy

Author

Gary W. Adamson, Aug 26 2007

Status

approved