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A073153 Triangle of numbers relating two sequences A073155 and A073156.

%I A073153 #9 Nov 18 2024 22:30:50
%S A073153 1,1,2,4,5,9,14,18,22,36,56,70,86,100,156,237,293,349,405,461,698,
%T A073153 1046,1283,1507,1703,1927,2164,3210,4762,5808,6756,7540,8324,9272,
%U A073153 10318,15080,22198,26960,31144,34462,37598,40916,45100,49862,72060,105430,127628
%N A073153 Triangle of numbers relating two sequences A073155 and A073156.
%F A073153 Triangle {T(n, k), n >= 0, 0<=k<=n} defined by:  T(0, 0)=1,
%F A073153 T(n, 0) = A073155(n),  T(n, n) = A073156(n),
%F A073153 T(n, 0) = T(n-1, n-1) + 2*T(n-2, n-2) + T(n-3, n-3),
%F A073153 T(n, k) = Sum_{j=0..k} A073155(j) * A073155(n-j).
%e A073153 T(4,0) = T(3,3) + 2*T(2,2) + T(1,1) = 2 + 2*9 + 36 = 56.
%e A073153 T(5,2) = A073155(0)*A073155(5) + A073155(1)*A073155(4) + A073155(2)*A073155(3) = 1*237 + 1*56 + 4*14 = 349.
%e A073153 Triangle begins:
%e A073153 1;
%e A073153 1, 2;
%e A073153 4, 5, 9;
%e A073153 14, 18, 22, 36;
%e A073153 56, 70, 86, 100, 156;
%e A073153 237, 293, 349, 405, 461, 698;
%e A073153 1046, 1283, 1507, 1703, 1927, 2164, 3210; ...
%Y A073153 Cf. A073154, A073155, A073156, A073157, A073153.
%K A073153 easy,nonn,tabl
%O A073153 0,3
%A A073153 _Paul D. Hanna_, Jul 29 2002
%E A073153 Formulas simplified by _Paul D. Hanna_, Nov 26 2012
%E A073153 a(31) onward corrected by _Sean A. Irvine_, Nov 18 2024