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A073153 Triangle of numbers relating two sequences A073155 and A073156. 5

%I

%S 1,1,2,4,5,9,14,18,22,36,56,70,86,100,156,237,293,349,405,461,698,

%T 1046,1283,1507,1703,1927,2164,3210,4762,5808,6756,6980,7204,8152,

%U 9198,13960,21078

%N Triangle of numbers relating two sequences A073155 and A073156.

%F Triangle {T(n, k), n >= 0, 0<=k<=n} defined by: T(0, 0)=1,

%F T(n, 0) = A073155(n), T(n, n) = A073156(n),

%F T(n, 0) = T(n-1, n-1) + 2*T(n-2, n-2) + T(n-3, n-3),

%F T(n, k) = Sum_{j=0..k} A073155(j) * A073155(n-j).

%e T(4,0) = T(3,3) + 2*T(2,2) + T(1,1) = 2 + 2*9 + 36 = 56.

%e T(5,2) = A073155(0)*A073155(5) + A073155(1)*A073155(4) + A073155(2)*A073155(3) = 1*237 + 1*56 + 4*14 = 349.

%e Triangle begins:

%e 1;

%e 1, 2;

%e 4, 5, 9;

%e 14, 18, 22, 36;

%e 56, 70, 86, 100, 156;

%e 237, 293, 349, 405, 461, 698;

%e 1046, 1283, 1507, 1703, 1927, 2164, 3210; ...

%Y Cf. A073154, A073155, A073156, A073157, A073153.

%K easy,nonn,tabl

%O 0,3

%A _Paul D. Hanna_, Jul 29 2002

%E Formulas simplified by _Paul D. Hanna_, Nov 26 2012

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Last modified February 7 10:10 EST 2023. Contains 360115 sequences. (Running on oeis4.)