login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A201730 Triangle T(n,k), read by rows, given by (2,1/2,3/2,0,0,0,0,0,0,0,...) DELTA (0,1/2,-1/2,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. 14
1, 2, 0, 5, 1, 0, 14, 6, 0, 0, 41, 26, 1, 0, 0, 122, 100, 10, 0, 0, 0, 365, 363, 63, 1, 0, 0, 0, 1094, 1274, 322, 14, 0, 0, 0, 0, 3281, 4372, 1462, 116, 1, 0, 0, 0, 0, 9842, 14760, 6156, 744, 18, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Riordan array ((1-2x)/(1-4x+3x^2),x^2/(1-4x+3x^2)).

A007318*A201701 as lower triangular matrices.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

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

Sum_{k, 0<=k<=n} T(n,k)*x^k = A139011(n), A000079(n), A007051(n), A006012(n), A001075(n), A081294(n), A001077(n), A084059(n), A108851(n), A084128(n), A081340(n), A084132(n) for x = -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively.

Sum_{k, k>+0} T(n+k,k) = A081704(n) .

T(n,k) = 3*T(n-1,k)+ Sum_{j>0} T(n-1-j,k-1).

T(n,k) = 4*T(n-1,k)+ T(n-2,k-1) - 3*T(n-2,k) with T(0,0)=1, T(1,0)= 2, T(1,1) = 0 and T(n,k) = 0 if k<0 or if n<k.

EXAMPLE

Triangle begins:

1

2, 0

5, 1, 0

14, 6, 0, 0

41, 26, 1, 0, 0

122, 100, 10, 0, 0, 0

365, 363, 63, 1, 0, 0, 0

MAPLE

A201730 := proc(n, k)

    (1-2*x)/(1-4*x+(3-y)*x^2) ;

    coeftayl(%, y=0, k) ;

    coeftayl(%, x=0, n) ;

end proc:

seq(seq(A201730(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Dec 06 2011

CROSSREFS

Cf. A007051 (1st column), A261064 (2nd column).

Sequence in context: A117780 A155759 A202209 * A188449 A177267 A188445

Adjacent sequences:  A201727 A201728 A201729 * A201731 A201732 A201733

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Dec 04 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified August 21 00:45 EDT 2017. Contains 290855 sequences.