A131352 Row sums of triangle A133935.

1, 2, 6, 14, 32, 72, 160, 352, 768, 1664, 3584, 7680, 16384, 34816, 73728, 155648, 327680, 688128, 1441792, 3014656, 6291456, 13107200, 27262976, 56623104, 117440512, 243269632, 503316480, 1040187392, 2147483648, 4429185024, 9126805504, 18790481920, 38654705664

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

Binomial transform of A093178: (1, 1, 3, 1, 5, 1, 7, 1...).

From R. J. Mathar, Dec 13 2008: (Start)

a(n) = A129954(n), n > 1.

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

a(n) = 2^(n-2)*(n+4) for n > 1. - Colin Barker, Jun 05 2012

From Amiram Eldar, Dec 19 2025: (Start)

Sum_{n>=0} 1/a(n) = 64*log(2) - 1277/30.

Sum_{n>=0} (-1)^n/a(n) = 797/30 - 64*log(3/2). (End)

Example

a(3) = 14 = sum of row 3 terms of triangle A133935: (1 + 3 + 9 + 1) = (1, 3, 3, 1) dot (1, 1, 3, 1).

Mathematica

CoefficientList[Series[(1-2x+2x^2-2x^3)/(1-2x)^2, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -4}, {1, 2, 6, 14}, 40] (* Harvey P. Dale, Dec 04 2021 *)

Crossrefs

Cf. A093178, A129954, A133935.

Sequence in context: A096238 A074878 A065495 * A232230 A294780 A051485

Adjacent sequences: A131349 A131350 A131351 * A131353 A131354 A131355

Keyword

nonn,easy

Author

Gary W. Adamson, Sep 29 2007

Extensions

Extended by R. J. Mathar, Dec 13 2008

Status

approved