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%I #31 Jun 07 2023 08:31:26
%S 7,22,52,112,239,494,1004,2024,4071,8166,16356,32736,65503,131038,
%T 262108,524248,1048535,2097110,4194260,8388560,16777167,33554382,
%U 67108812,134217672,268435399,536870854,1073741764,2147483584,4294967231,8589934526,17179869116,34359738296
%N Records in A101119, which forms the nonzero differences of A006519 and A003484.
%H Harvey P. Dale, <a href="/A101120/b101120.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,1,-3,2).
%F a(n) = A101119(2^(n-1)) for n>=1.
%F a(n) = 2^(n+3) - 2^((n-1)(mod 4)) - 8*floor((n+3)/4).
%F a(n) = 2^(n+3) - A003485(n+3). - _Johannes W. Meijer_, Oct 31 2012
%F From _Chai Wah Wu_, Apr 15 2017: (Start)
%F a(n) = 3*a(n-1) - 2*a(n-2) + a(n-4) - 3*a(n-5) + 2*a(n-6) for n > 6.
%F G.f.: x*(-x - 7)/((x - 1)^2*(x + 1)*(2*x - 1)*(x^2 + 1)). (End)
%F E.g.f.: (exp(x)*(32*exp(x) - 8*x - 27) - 4*cos(x) - cosh(x) - 2*sin(x) + sinh(x))/4. - _Stefano Spezia_, Jun 06 2023
%t LinearRecurrence[{3,-2,0,1,-3,2},{7,22,52,112,239,494},30] (* _Harvey P. Dale_, Jan 23 2023 *)
%o (PARI) a(n)=2^(n+3)-2^((n-1)%4)-8*((n+3)\4)
%o (Python)
%o def A101120(n): return (1<<(n+3))-(1<<((n-1)&3))-(((n+3)&-4)<<1) # _Chai Wah Wu_, Jul 10 2022
%Y Cf. A003484, A006519, A101119, A101121, A101122.
%K nonn,easy
%O 1,1
%A _Simon Plouffe_ and _Paul D. Hanna_, Dec 02 2004
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