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%I #25 Mar 17 2024 12:55:33
%S 3,7,18,50,145,429,1280,3832,11487,34451,103342,310014,930029,2790073,
%T 8370204,25110596,75331771,225995295,677985866,2033957578,6101872713,
%U 18305618117,54916854328,164750562960,494251688855,1482755066539
%N a(n) = (7*3^n + 2n + 5)/4.
%C A floretion-generated sequence relating sequences A007051 and A047926. (a(n)) results from a force transform of the sequence of powers of 3.
%C Floretion Algebra Multiplication Program, FAMP Code: 4jesleftforseq[A*B] with A = - .25'i - .25i' - .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .25e and B = + 'i + .5j' + .5k' + .5'ij' + .5'ik', 1vesforseq[A*B](n) = 3^(n+1), ForType: 1A.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,3).
%F a(n) = 2*A007051(n) + A047926(n).
%F a(n) = 5*a(n-1)-7*a(n-2)+3*a(n-3). G.f.: (3-2*x)*(1-2*x)/((1-x)^2*(1-3*x)). [_Colin Barker_, Aug 28 2012]
%t Table[(7*3^n+2*n+5)/4,{n,0,25}] (* _Harvey P. Dale_, Feb 23 2011 *)
%Y Cf. A007051, A047926.
%K nonn,easy
%O 0,1
%A _Creighton Dement_, Mar 17 2005
%E More terms from _Harvey P. Dale_, Feb 23 2011
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