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A048773
Partial sums of A048697.
0
1, 11, 32, 84, 209, 511, 1240, 3000, 7249, 17507, 42272, 102060, 246401, 594871, 1436152, 3467184, 8370529, 20208251, 48787040, 117782340, 284351729, 686485807, 1657323352, 4001132520, 9659588401, 23320309331, 56300207072, 135920723484, 328141654049
OFFSET
0,2
FORMULA
a(n) = 2*a(n-1)+a(n-2)+9; a(0)=1, a(1)=11.
a(n) = (((10+(11/2)*sqrt(2))*(1+sqrt(2))^n - (10-(11/2)*sqrt(2))*(1-sqrt(2))^n)/ 2*sqrt(2))-9/2.
From R. J. Mathar, Nov 08 2012: (Start)
G.f.: ( 1+8*x ) / ( (x-1)*(x^2+2*x-1) ).
a(n) = A048739(n)+8*A048739(n-1). (End)
a(n) = 3*a(n-1)-a(n-2)-a(n-3). - Wesley Ivan Hurt, May 21 2021
MATHEMATICA
Accumulate[LinearRecurrence[{2, 1}, {1, 10}, 35]] (* Harvey P. Dale, Jul 26 2011 *)
LinearRecurrence[{3, -1, -1}, {1, 11, 32}, 29] (* Ray Chandler, Aug 03 2015 *)
CROSSREFS
KEYWORD
easy,nice,nonn
EXTENSIONS
More terms from Harvey P. Dale, Jul 26 2011
STATUS
approved