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A099093 Riordan array (1, 3+3x).

%I A099093 #21 Jan 15 2025 01:45:45
%S A099093 1,0,3,0,3,9,0,0,18,27,0,0,9,81,81,0,0,0,81,324,243,0,0,0,27,486,1215,
%T A099093 729,0,0,0,0,324,2430,4374,2187,0,0,0,0,81,2430,10935,15309,6561,0,0,
%U A099093 0,0,0,1215,14580,45927,52488,19683,0,0,0,0,0,243,10935,76545,183708,177147,59049
%N A099093 Riordan array (1, 3+3x).
%C A099093 Row sums are A030195. Diagonal sums are A099094.
%C A099093 The Riordan array (1,s+tx) defines T(n,k) = binomial(k,n-k)s^k(t/s)^(n-k). The row sums satisfy a(n)=s*a(n-1)+t*a(n-2) and the diagonal sums satisfy a(n)=s*a(n-2)+t*a(n-3).
%C A099093 Modulo 2, this sequence gives A106344. - _Philippe Deléham_, Dec 18 2008
%F A099093 T(n,k) = binomial(k, n-k)*3^k. - corrected by _Michel Marcus_, Feb 21 2015
%F A099093 Columns have g.f. (3x+3x^3)^k.
%F A099093 T(n,k) = A026729(n,k)*3^k. - _Philippe Deléham_, Jul 29 2006
%e A099093 Rows begin:
%e A099093   1;
%e A099093   0, 3;
%e A099093   0, 3, 9;
%e A099093   0, 0, 18, 27;
%e A099093   0, 0, 9, 81, 81;
%e A099093   0, 0, 0, 81, 324, 243;
%e A099093   0, 0, 0, 27, 486, 1215, 729;
%e A099093   ...
%o A099093 (PARI) tabl(nn) = {for (n=0, nn, for (k=0, n, print1(binomial(k, n-k)*3^k, ", ");); print(););} \\ _Michel Marcus_, Feb 21 2015
%o A099093 (Magma) [[Binomial(k,n-k)*3^k: k in [0..n]]: n in [0.. 10]]; // _Vincenzo Librandi_, Feb 21 2015 /* as the triangle */
%Y A099093 Cf. A038221.
%K A099093 easy,nonn,tabl
%O A099093 0,3
%A A099093 _Paul Barry_, Sep 25 2004