OFFSET
1,4
COMMENTS
From Philippe Deléham, Feb 16 2014: (Start)
As a Riordan array, this is (1/(1 - x - x^2 - x^3 - x^4), x/(1 - x - x^2 - x^3 - x^4)).
Row sums are A103142(n).
Diagonal sums are A077926(n)*(-1)^n.
Tetranacci convolution triangle. (End)
FORMULA
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.
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
EXAMPLE
Triangle begins:
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;
PROG
(Maxima)
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);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Dec 14 2011
STATUS
approved