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!)
A202193 Triangle T(n,m) = coefficient of x^n in expansion of (x/(1 - x - x^2 - x^3 - x^4))^m = Sum_{n>=m} T(n,m) x^n. 1

%I #18 Jul 21 2021 07:15:44

%S 1,1,1,2,2,1,4,5,3,1,8,12,9,4,1,15,28,25,14,5,1,29,62,66,44,20,6,1,56,

%T 136,165,129,70,27,7,1,108,294,401,356,225,104,35,8,1,208,628,951,944,

%U 676,363,147,44,9,1,401,1328,2211,2424,1935,1176,553,200

%N Triangle T(n,m) = coefficient of x^n in expansion of (x/(1 - x - x^2 - x^3 - x^4))^m = Sum_{n>=m} T(n,m) x^n.

%C From _Philippe Deléham_, Feb 16 2014: (Start)

%C As a Riordan array, this is (1/(1 - x - x^2 - x^3 - x^4), x/(1 - x - x^2 - x^3 - x^4)).

%C T(n,0) = A000078(n+3); T(n+1,1) = A118898(n+4).

%C Row sums are A103142(n).

%C Diagonal sums are A077926(n)*(-1)^n.

%C Tetranacci convolution triangle. (End)

%F T(n,m) = Sum_{k=1..n-m} Sum_{i=0..floor((n-m-k)/4)} (-1)^i*binomial(k,k-i)*binomial(n-m-4*i-1,k-1))*binomial(k+m-1,m-1)), n > m, T(n,n)=1.

%F T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-3,k) + T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k < 0 or if k > n. - _Philippe Deléham_, Feb 16 2014

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 2, 1;

%e 4, 5, 3, 1;

%e 8, 12, 9, 4, 1;

%e 15, 28, 25, 14, 5, 1;

%e 29, 62, 66, 44, 20, 6, 1;

%o (Maxima)

%o T(n,m):=if n=m then 1 else sum(sum((-1)^i*binomial(k,k-i)*binomial(n-m-4*i-1,k-1),i,0,(n-m-k)/4)*binomial(k+m-1,m-1),k,1,n-m);

%Y Cf. Similar sequences : A037027 (Fibonacci convolution triangle), A104580 (tribonacci convolution triangle). - _Philippe Deléham_, Feb 16 2014

%K nonn,tabl

%O 1,4

%A _Vladimir Kruchinin_, Dec 14 2011

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 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)