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A316076 Sequence shifts left four places under Weigh transform with a(n) = signum(n) for n<4.

%I A316076 #10 May 09 2019 06:58:20
%S A316076 0,1,1,1,1,1,1,2,2,3,4,6,8,12,18,26,39,58,88,133,202,308,472,725,1116,
%T A316076 1725,2669,4141,6437,10027,15643,24448,38265,59979,94143,147953,
%U A316076 232799,366725,578311,912913,1442503,2281429,3611406,5721528,9071789,14394837
%N A316076 Sequence shifts left four places under Weigh transform with a(n) = signum(n) for n<4.
%H A316076 Alois P. Heinz, <a href="/A316076/b316076.txt">Table of n, a(n) for n = 0..2000</a>
%F A316076 G.f.: x + x^2 + x^3 + x^4 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019
%p A316076 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316076       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A316076     end:
%p A316076 a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(4):
%p A316076 seq(a(n), n=0..45);
%Y A316076 Column k=4 of A316074.
%Y A316076 Cf. A057427, A218021.
%K A316076 nonn,eigen
%O A316076 0,8
%A A316076 _Alois P. Heinz_, Jun 23 2018