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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
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, 136, 165, 129, 70, 27, 7, 1, 108, 294, 401, 356, 225, 104, 35, 8, 1, 208, 628, 951, 944, 676, 363, 147, 44, 9, 1, 401, 1328, 2211, 2424, 1935, 1176, 553, 200 (list; table; graph; refs; listen; history; text; internal format)
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)).

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

Row sums are A103142(n).

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

Tetranacci convolution triangle. (End)

LINKS

Table of n, a(n) for n=1..63.

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

Cf. Similar sequences : A037027 (Fibonacci convolution triangle), A104580 (Tribonacci convolution triangle). - Philippe Deléham, Feb 16 2014

Sequence in context: A272888 A001404 A104580 * A105306 A183191 A273713

Adjacent sequences:  A202190 A202191 A202192 * A202194 A202195 A202196

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Dec 14 2011

STATUS

approved

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Last modified February 20 04:12 EST 2020. Contains 332063 sequences. (Running on oeis4.)