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
Offset: 0
Examples
a(3) = 14 = sum of row 3 terms of triangle A133935: (1 + 3 + 9 + 1); = (1, 3, 3, 1) dot (1, 1, 3, 1).
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-4).
Programs
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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 *)
Formula
Binomial transform of A093178: (1, 1, 3, 1, 5, 1, 7, 1...)
a(n) = A129954(n), n>1. G.f.: (1-2x+2x^2-2x^3)/(1-2x)^2. [R. J. Mathar, Dec 13 2008]
a(n) = 2^(n-2)*(n+4) for n>1. - _Colin Barker, Jun 05 2012
Extensions
Extended by R. J. Mathar, Dec 13 2008