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%I #26 Apr 18 2023 17:41:43
%S 1,3,7,11,27,33,69,77,141,151,251,263,407,421,617,633,889,907,1231,
%T 1251,1651,1673,2157,2181,2757,2783,3459,3487,4271,4301,5201,5233,
%U 6257,6291,7447,7483,8779,8817,10261,10301,11901,11943,13707,13751,15687,15733,17849
%N Add/multiply sequence, see example.
%C It appears that a(2*n+1) = 2*(n + A002623(2*n-1)) + 3. - _Carl Najafi_, Jan 21 2013
%H Harvey P. Dale, <a href="/A093361/b093361.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F a(n) = (1/24)*(4*n^3 + 12*n^2 + 20*n + 33 + (6*n^2 - 9)*(-1)^n). - _Ralf Stephan_, Dec 02 2004
%F G.f.: (1 + 2*x + x^2 - 2*x^3 + 7*x^4 - x^6)/((1 + x)^3*(x - 1)^4). - _R. J. Mathar_, May 20 2013
%F E.g.f.: ((12 + 15*x + 15*x^2 + 2*x^3)*cosh(x) + (21 + 21*x + 9*x^2 + 2*x^3)*sinh(x))/12. - _Stefano Spezia_, Apr 18 2023
%e a(0) = 1
%e a(1) = 1+2
%e a(2) = 1+2*3
%e a(3) = 1+2*3+4
%e a(4) = 1+2*3+4*5
%e a(5) = 1+2*3+4*5+6
%e a(6) = 1+2*3+4*5+6*7
%e a(7) = 1+2*3+4*5+6*7+8
%e a(8) = 1+2*3+4*5+6*7+8*9
%t LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,3,7,11,27,33,69},50] (* _Harvey P. Dale_, Jun 02 2019 *)
%Y Cf. A002623.
%K nonn,easy
%O 0,2
%A _Jorge Coveiro_, Apr 28 2004
%E More terms from _Ralf Stephan_, Dec 02 2004
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