cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A276990 a(n) = (phi; phi)_n + (1-phi; 1-phi)_n, where (q; q)_n is the q-Pochhammer symbol, phi = (1+sqrt(5))/2 is the golden ratio.

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%I A276990 #9 Feb 16 2025 08:33:36
%S A276990 2,1,2,-2,20,-190,3240,-90800,4174920,-313173840,38204662320,
%T A276990 -7564715117520,2428250059593600,-1262694691720176000,
%U A276990 1063187432567808662400,-1449125250052431355430400,3196769645011428154428883200,-11412468527893653264760022630400
%N A276990 a(n) = (phi; phi)_n + (1-phi; 1-phi)_n, where (q; q)_n is the q-Pochhammer symbol, phi = (1+sqrt(5))/2 is the golden ratio.
%H A276990 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>, <a href="https://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>.
%F A276990 (phi; phi)_n = (a(n) + A276991(n)*sqrt(5))/2.
%F A276990 (1-phi; 1-phi)_n = (a(n) - A276991(n)*sqrt(5))/2.
%F A276990 a(n) ~ c * (-1)^n * phi^(n*(n+1)/2), where c = (1/phi)_inf = A276987 = 0.1208019218617061294237231569887920563043992516794...
%t A276990 Round@Table[QPochhammer[GoldenRatio, GoldenRatio, n] + QPochhammer[1 - GoldenRatio, 1 - GoldenRatio, n], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
%Y A276990 Cf. A274983, A276474, A276987, A276991.
%K A276990 sign
%O A276990 0,1
%A A276990 _Vladimir Reshetnikov_, Sep 24 2016