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1, 9, 26, 68, 169, 413, 1002, 2424, 5857, 14145, 34154, 82460, 199081, 480629, 1160346, 2801328, 6763009, 16327353, 39417722, 95162804, 229743337, 554649485, 1339042314, 3232734120, 7804510561, 18841755249, 45488021066, 109817797388, 265123615849
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refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..28.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-1)
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FORMULA
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a(n)=2*a(n-1)+a(n-1)+7; a(0)=1, a(1)=9.
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
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
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EXAMPLE
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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.
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MATHEMATICA
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Table[6*Fibonacci[n, 2] + Fibonacci[n+1, 2], {n, 0, 22}] // Accumulate (* Jean-François Alcover, Mar 25 2013 *)
Accumulate[LinearRecurrence[{2, 1}, {1, 8}, 40]] (* or *) LinearRecurrence[ {3, -1, -1}, {1, 9, 26}, 40] (* Harvey P. Dale, May 01 2013 *)
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CROSSREFS
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Cf. A001333, A000129, A048694, A048695.
Sequence in context: A270695 A048468 A255108 * A055849 A235163 A084813
Adjacent sequences: A048768 A048769 A048770 * A048772 A048773 A048774
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Barry E. Williams
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EXTENSIONS
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More terms from Harvey P. Dale, May 01 2013
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STATUS
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approved
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