login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164942 Triangle, read by rows, T(n,k) = (-1)^k*binomial(n, k)*3^(n-k). 4
1, 3, -1, 9, -6, 1, 27, -27, 9, -1, 81, -108, 54, -12, 1, 243, -405, 270, -90, 15, -1, 729, -1458, 1215, -540, 135, -18, 1, 2187, -5103, 5103, -2835, 945, -189, 21, -1, 6561, -17496, 20412, -13608, 5670, -1512, 252, -24, 1, 19683, -59049, 78732, -61236, 30618, -10206, 2268, -324, 27, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Rows sum up to A000079, antidiagonals sum up to A001906.
Triangle, read by rows, given by [3,0,0,0,0,0,0,0,...] DELTA [ -1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Sep 02 2009
Row n: expansion of (3-x)^n. - Philippe Deléham, Oct 09 2011
Essentially the same as the inverse of A027465, but with opposite signs in every other row. - M. F. Hasler, Feb 17 2020
The inverse of A027465 is (-1)^(n-k)*binomial(n, k)*3^(n - k). - G. C. Greubel, Feb 17 2020
LINKS
FORMULA
T(n,k) = (-1)^n*(Inverse of A027465).
T(n,k) = 3*T(n-1,k) - T(n-1,k-1). - Philippe Deléham, Oct 09 2011
G.f.: 1/(1-3*x+x*y). - R. J. Mathar, Aug 11 2015
EXAMPLE
Begins as triangle:
1;
3, -1;
9, -6, 1;
27, -27, 9, -1;
81, -108, 54, -12, 1;
243, -405, 270, -90, 15, -1;
MAPLE
seq(seq( (-1)^k*binomial(n, k)*3^(n-k), k=0..n), n=0..10); # G. C. Greubel, Feb 17 2020
MATHEMATICA
With[{m = 9}, CoefficientList[CoefficientList[Series[1/(1-3*x+x*y), {x, 0, m}, {y, 0, m}], x], y]] // Flatten (* Georg Fischer, Feb 17 2020 *)
PROG
(Magma) [(-1)^k*Binomial(n, k)*3^(n-k): k in [0..n], n in [0..10]]; // G. C. Greubel, Feb 17 2020
(Sage) [[(-1)^k*binomial(n, k)*3^(n-k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Feb 17 2020
CROSSREFS
Sequence in context: A105545 A178831 A027465 * A236420 A187537 A246256
KEYWORD
sign,tabl
AUTHOR
Mark Dols, Sep 01 2009
EXTENSIONS
More terms from Philippe Deléham, Oct 09 2011
a(46) corrected by Georg Fischer, Feb 17 2020
Title changed by G. C. Greubel, Feb 17 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)