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Partial sums of A048695.
1

%I #12 Jun 13 2015 00:50:00

%S 1,9,26,68,169,413,1002,2424,5857,14145,34154,82460,199081,480629,

%T 1160346,2801328,6763009,16327353,39417722,95162804,229743337,

%U 554649485,1339042314,3232734120,7804510561,18841755249,45488021066,109817797388,265123615849

%N Partial sums of A048695.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-1)

%F a(n)=2*a(n-1)+a(n-1)+7; a(0)=1, a(1)=9.

%F G.f. ( 1+6*x ) / ( (x-1)*(x^2+2*x-1) ). a(n)=A048739(n)+6*A048739(n-1). - _R. J. Mathar_, Nov 08 2012

%F a(0)=1, a(1)=9, a(2)=26, a(n)=3*a(n-1)-a(n-2)-a(n-3). - _Harvey P. Dale_, May 01 2013

%e a(n)=[ {(8+(9/2)*sqrt(2))(1+sqrt(2))^n -(8-(9/2)*sqrt(2))(1-sqrt(2))^n}/ 2*sqrt(2) ]-7/2.

%t Table[6*Fibonacci[n, 2] + Fibonacci[n+1, 2], {n, 0, 22}] // Accumulate (* _Jean-François Alcover_, Mar 25 2013 *)

%t Accumulate[LinearRecurrence[{2,1},{1,8},40]] (* or *) LinearRecurrence[ {3,-1,-1},{1,9,26},40] (* _Harvey P. Dale_, May 01 2013 *)

%Y Cf. A001333, A000129, A048694, A048695.

%K easy,nice,nonn

%O 0,2

%A _Barry E. Williams_

%E More terms from _Harvey P. Dale_, May 01 2013