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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124182 A skewed version of triangular array A081277. 9

%I

%S 1,0,1,0,1,2,0,0,3,4,0,0,1,8,8,0,0,0,5,20,16,0,0,0,1,18,48,32,0,0,0,0,

%T 7,56,112,64,0,0,0,0,1,32,160,256,128,0,0,0,0,0,9,120,432,576,256,0,0,

%U 0,0,0,1,50,400,1120,1280,512

%N A skewed version of triangular array A081277.

%C Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, -1, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 0, 0, 0, 0, 0, 0, 0,...] where DELTA is the operator defined in A084938 . Falling diagonal sums in A052980.

%F T(0,0)=T(1,1)=1, T(n,k)=0 if n<k or if k<0,T(n,k)=T(n-2,k-1)+2*T(n-1,k-1) . Sum_{k, 0<=k<=n}x^k*T(n,k)= (-1)^n*A090965(n), (-1)^n*A084120(n), (-1)^n*A006012(n), A033999(n), A000007(n), A001333(n), A084059(n) for x= -4, -3, -2, -1, 0, 1, 2 respectively . Sum_{k, 0<=k<=[n/2]} T(n-k,k)= Fibonacci(n-1)= A000045(n-1).

%F Sum_{k, 0<=k<=n}T(n,k)*x^(n-k)= A000012(n), A011782(n), A001333(n), A026150(n), A046717(n), A084057(n), A002533(n), A083098(n), A084058(n), A003665(n), A002535(n), A133294(n), A090042(n), A125816(n), A133343(n), A133345(n), A120612(n), A133356(n), A125818(n) for x= -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 respectively . - _Philippe Deléham_, Dec 26 2007

%F Sum_{k, 0<=k<=n}T(n,k)*(-x)^(n-k)= A011782(n), A000012(n), A146559(n), A087455(n), A138230(n), A006495(n), A138229(n) for x= 0,1,2,3,4,5,6 respectively. [From _Philippe Deléham_, Nov 14 2008]

%F G.f.: (1-y*x)/(1-2y*x-y*x^2). - _Philippe Deléham_, Dec 04 2011

%F Sum_{k, 0<=k<=n} T(n,k)^2 = A002002(n) for n>0. - _Philippe Deléham_, Dec 04 2011

%e Triangle begins:

%e .1;

%e .0, 1;

%e .0, 1, 2;

%e .0, 0, 3, 4;

%e .0, 0, 1, 8, 8;

%e .0, 0, 0, 5, 20, 16;

%e .0, 0, 0, 1, 18, 48, 32;

%e .0, 0, 0, 0, 7, 56, 112, 64;

%e .0, 0, 0, 0, 1, 32, 160, 256, 128;

%e .0, 0, 0, 0, 0, 9, 120, 432, 576, 256;

%e .0, 0, 0, 0, 0, 1, 50, 400, 1120, 1280, 512;

%Y Cf. A025192 (column sums). Diagonals include : A011782, A001792, A001793, A001794, A006974, A006975, A006976

%K nonn,tabl

%O 0,6

%A _Philippe Deléham_, Dec 05 2006

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)