A144172 - OEIS

%I #2 Mar 30 2012 17:25:32

%S 1,1,1,1,1,2,0,1,2,4,1,0,2,4,7,0,1,0,4,7,14,0,0,2,0,7,14,26,1,0,0,4,0,

%T 14,26,49,0,1,0,0,7,0,26,49,94,0,0,2,0,0,14,0,49,94,177,0,0,0,4,0,0,

%U 26,0,94,177,336,0,0,0,0,7,0,0,49,0,177,336,637

%N Eigentriangle, row sums = A076739, the number of compositions into Fibonacci numbers.

%C Row sums = A076739 starting with offset 1: (1, 2, 4, 7, 14, 26, 49,...).

%C Left border = A010056, the characteristic function of the Fibonacci numbers Starting with offset 1: (1, 1, 1, 0, 1,...).

%C Sum of n-th row terms = rightmost term of next row.

%C Right border = A076739.

%F T(n,k) = A010056(n-k+1)*A076739(k-1). A010056, the characteristic function of the Fibonacci numbers, starts with offset 1: (1, 1, 1, 0, 1,...). A076739(k-1), the INVERTi transform of (1, 1, 1, 0, 1,...) starts with offset 0: (1, 1, 2, 4, 7, 14,...).

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 1, 1, 2;

%e 0, 1, 2, 4;

%e 1, 0, 2, 4, 7;

%e 0, 1, 0, 4, 7, 14;

%e 0, 0, 2, 0, 7, 14, 26;

%e 1, 0, 0, 4, 0, 14, 26, 49;

%e 0, 1, 0, 0, 7, 0, 26, 49, 94;

%e 0, 0, 2, 0, 0, 14, 0, 49, 94, 177;

%e 0, 0, 0, 4, 0, 0, 26, 0, 94, 177, 336;

%e 0, 0, 0, 0, 7, 0, 0, 49, 0, 177, 336, 637;

%e 1, 0, 0, 0, 0, 14, 0, 0, 94, 0, 336, 637, 1206;

%e ...

%e Example: row 5 = (1, 0, 2, 4, 7) = termwise product of (1, 0, 1, 1, 1) and (1, 1, 2, 4, 7).

%Y A076739, Cf. A010056

%K nonn,tabl

%O 1,6

%A _Gary W. Adamson_, Sep 12 2008