[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Sequence shifts left three places under Weigh transform with a(n) = signum(n) for n<3.
5

%I #10 May 09 2019 06:52:50

%S 0,1,1,1,1,1,2,2,3,5,7,10,17,26,40,65,104,166,272,442,720,1186,1954,

%T 3222,5346,8881,14778,24668,41254,69088,115959,194925,328123,553200,

%U 933944,1578614,2671656,4526654,7677736,13035809,22154806,37687152,64165838

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

%H Alois P. Heinz, <a href="/A316075/b316075.txt">Table of n, a(n) for n = 0..2000</a>

%F G.f.: x + x^2 + x^3 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

%p end:

%p a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(3):

%p seq(a(n), n=0..42);

%Y Column k=3 of A316074.

%Y Cf. A057427, A218020.

%K nonn,eigen

%O 0,7

%A _Alois P. Heinz_, Jun 23 2018