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%I #36 Oct 03 2023 19:06:34
%S 1,6,16,36,76,156,316,636,1276,2556,5116,10236,20476,40956,81916,
%T 163836,327676,655356,1310716,2621436,5242876,10485756,20971516,
%U 41943036,83886076,167772156,335544316,671088636,1342177276,2684354556,5368709116,10737418236,21474836476
%N a(n) = T(4,n), array T given by A048483.
%C Row sums of triangle A131113. - _Gary W. Adamson_, Jun 15 2007
%C a(n) = sum of (n+1)-th row terms of triangle A134636. This sequence is the binomial transform of 1, 5, 5, (5 continued). - _Gary W. Adamson_, Nov 04 2007
%C Row sums of triangle A135856. - _Gary W. Adamson_, Dec 01 2007
%H Vincenzo Librandi, <a href="/A048487/b048487.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = 5*2^n - 4. - _Henry Bottomley_, May 29 2001
%F a(n) = 2*a(n-1) + 4 for n > 0 with a(0) = 1. - _Paul Barry_, Aug 25 2004
%F From _Colin Barker_, Sep 13 2012: (Start)
%F a(n) = 3*a(n-1) - 2*a(n-2) for n >= 2.
%F G.f.: (1 + 3*x)/((1 - x)*(1 - 2*x)). (End)
%F a(n) = A123208(2*n). - _Philippe Deléham_, Apr 15 2013
%F E.g.f.: exp(x)*(5*exp(x) - 4). - _Stefano Spezia_, Oct 03 2023
%t a=1; lst={a}; k=5; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 15 2008 *)
%t a=6; lst={1, a}; k=10; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008 *)
%o (Magma)[5*2^n-4: n in [0..30]]; // _Vincenzo Librandi_, Sep 23 2011
%Y Cf. A010716 (n-th difference of a(n), a(n-1), ..., a(0)).
%Y Diagonal of A062001.
%Y A column of A119726.
%Y Cf. A048483, A123208, A131113, A134636, A135856.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_
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