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A129094 a(n) = A030067(2^n + 2^(n-1) - 1) for n>=1, where A030067 gives the semi-Fibonacci numbers.

%I A129094 #3 Mar 30 2012 18:37:03
%S A129094 1,3,9,35,189,1523,19409,407067,14448821,886912635,95777365753,
%T A129094 18445977557011,6405629912921517,4047190499790323395,
%U A129094 4687597187390655089313,10017007133285072336267467
%N A129094 a(n) = A030067(2^n + 2^(n-1) - 1) for n>=1, where A030067 gives the semi-Fibonacci numbers.
%e A129094 This sequence equals the central terms of the triangle formed from the semi-Fibonacci numbers (A030067) with 2^n terms in row n for n>=1:
%e A129094 n=0: 1;
%e A129094 n=1: (1), 2;
%e A129094 n=2: 1, (3), 2, 5;
%e A129094 n=3: 1, 6, 3, (9), 2, 11, 5, 16;
%e A129094 n=4: 1, 17, 6, 23, 3, 26, 9, (35), 2, 37, 11, 48, 5, 53, 16, 69; ...
%e A129094 The semi-Fibonacci numbers (A030067) start:
%e A129094 [1, (1), 2, 1, (3), 2, 5, 1, 6, 3, (9), 2, 11, 5, 16, 1, ...],
%e A129094 and obey the recurrence:
%e A129094 A030067(n) = A030067(n/2) when n is even; and
%e A129094 A030067(n) = A030067(n-1) + A030067(n-2) when n is odd.
%o A129094 (PARI)
%Y A129094 Cf. A030067; A129092, A129093.
%K A129094 nonn
%O A129094 1,2
%A A129094 _Paul D. Hanna_, Mar 29 2007