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A316075 Sequence shifts left three places under Weigh transform with a(n) = signum(n) for n<3.

%I A316075 #10 May 09 2019 06:52:50
%S A316075 0,1,1,1,1,1,2,2,3,5,7,10,17,26,40,65,104,166,272,442,720,1186,1954,
%T A316075 3222,5346,8881,14778,24668,41254,69088,115959,194925,328123,553200,
%U A316075 933944,1578614,2671656,4526654,7677736,13035809,22154806,37687152,64165838
%N A316075 Sequence shifts left three places under Weigh transform with a(n) = signum(n) for n<3.
%H A316075 Alois P. Heinz, <a href="/A316075/b316075.txt">Table of n, a(n) for n = 0..2000</a>
%F A316075 G.f.: x + x^2 + x^3 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019
%p A316075 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316075       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A316075     end:
%p A316075 a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(3):
%p A316075 seq(a(n), n=0..42);
%Y A316075 Column k=3 of A316074.
%Y A316075 Cf. A057427, A218020.
%K A316075 nonn,eigen
%O A316075 0,7
%A A316075 _Alois P. Heinz_, Jun 23 2018