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A144172 Eigentriangle, row sums = A076739, the number of compositions into Fibonacci numbers.

%I A144172 #2 Mar 30 2012 17:25:32
%S A144172 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 A144172 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 A144172 26,0,94,177,336,0,0,0,0,7,0,0,49,0,177,336,637
%N A144172 Eigentriangle, row sums = A076739, the number of compositions into Fibonacci numbers.
%C A144172 Row sums = A076739 starting with offset 1: (1, 2, 4, 7, 14, 26, 49,...).
%C A144172 Left border = A010056, the characteristic function of the Fibonacci numbers Starting with offset 1: (1, 1, 1, 0, 1,...).
%C A144172 Sum of n-th row terms = rightmost term of next row.
%C A144172 Right border = A076739.
%F A144172 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 A144172 First few rows of the triangle =
%e A144172 1;
%e A144172 1, 1;
%e A144172 1, 1, 2;
%e A144172 0, 1, 2, 4;
%e A144172 1, 0, 2, 4, 7;
%e A144172 0, 1, 0, 4, 7, 14;
%e A144172 0, 0, 2, 0, 7, 14, 26;
%e A144172 1, 0, 0, 4, 0, 14, 26, 49;
%e A144172 0, 1, 0, 0, 7, 0, 26, 49, 94;
%e A144172 0, 0, 2, 0, 0, 14, 0, 49, 94, 177;
%e A144172 0, 0, 0, 4, 0, 0, 26, 0, 94, 177, 336;
%e A144172 0, 0, 0, 0, 7, 0, 0, 49, 0, 177, 336, 637;
%e A144172 1, 0, 0, 0, 0, 14, 0, 0, 94, 0, 336, 637, 1206;
%e A144172 ...
%e A144172 Example: row 5 = (1, 0, 2, 4, 7) = termwise product of (1, 0, 1, 1, 1) and (1, 1, 2, 4, 7).
%Y A144172 A076739, Cf. A010056
%K A144172 nonn,tabl
%O A144172 1,6
%A A144172 _Gary W. Adamson_, Sep 12 2008