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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

Contribution 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..(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

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 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)