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

 

Logo


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 June 25 22:15 EDT 2017. Contains 288730 sequences.