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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 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.)