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%I #22 Jun 29 2023 19:57:38
%S 2,3,8,18,40,88,192,416,896,1920,4096,8704,18432,38912,81920,172032,
%T 360448,753664,1572864,3276800,6815744,14155776,29360128,60817408,
%U 125829120,260046848,536870912,1107296256,2281701376,4697620480
%N Third differences of A129952.
%H Vincenzo Librandi, <a href="/A129955/b129955.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 (4, -4).
%F First differences of A129954: a(n) = A129954(n+1) - A129954(n).
%F a(n) = A034007(n+2)-2^(n-2) for n > 1.
%F a(0) = 2, a(1) = 3; for n > 1, a(n) = (n+6)*2^(n-2).
%F G.f.: (2-5*x+4*x^2-2*x^3)/(1-2*x)^2.
%F From _Amiram Eldar_, Jan 13 2021: (Start)
%F Sum_{n>=0} 1/a(n) = 256*log(2) - 12347/70.
%F Sum_{n>=0} (-1)^n/a(n) = 21851/210 - 256*log(3/2). (End)
%t Differences[LinearRecurrence[{4,-4},{1,1,2,6},40],3] (* _Harvey P. Dale_, Sep 04 2020 *)
%o (Magma) m:=17; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; T:=[ &+[ Binomial(j-1, k-1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; U:=[ T[n+1]-T[n]: n in[1..2*m-1] ]; V:=[ U[n+1]-U[n]: n in[1..2*m-2] ]; [ V[n+1]-V[n]: n in[1..2*m-3] ]; // _Klaus Brockhaus_, Jun 17 2007
%o (PARI) {m=29; print1(2, ",", 3, ","); for(n=2, m, print1((n+6)*2^(n-2), ","))} \\ _Klaus Brockhaus_, Jun 17 2007
%Y Cf. A129952, A129953, A129954, A034007.
%K nonn
%O 0,1
%A _Paul Curtz_, Jun 10 2007
%E Edited and extended by _Klaus Brockhaus_, Jun 17 2007
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