A130625 - OEIS

%I #17 Jan 01 2024 23:48:17

%S 1,4,7,11,20,41,85,172,343,683,1364,2729,5461,10924,21847,43691,87380,

%T 174761,349525,699052,1398103,2796203,5592404,11184809,22369621,

%U 44739244,89478487,178956971,357913940,715827881,1431655765,2863311532

%N First differences of A130624.

%C a(n) = A130624(n+1) - A130624(n).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2).

%F G.f.: (1-x)*(1+2*x)/((1-2*x)*(1-x+x^2)).

%F a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3). Sequence is identical to its third differences. Binomial transform of 1, 3, 0. - _Paul Curtz_, Nov 23 2007

%t LinearRecurrence[{3,-3,2},{1,4,7},40] (* _Harvey P. Dale_, Apr 27 2015 *)

%o (Magma) m:=33; S:=[ [0, 1, 3][ (n-1) mod 3 +1 ]: n in [1..m] ]; T:=[ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; [ T[n+1]-T[n]: n in[1..m-1] ]; /* _Klaus Brockhaus_, Jun 21 2007 */

%Y Cf. A130624, A130626 (second differences).

%K nonn

%O 0,2

%A _Paul Curtz_, Jun 18 2007

%E Edited and extended by _Klaus Brockhaus_, Jun 21 2007