A048771 Partial sums of A048695.

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

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-1)

Formula

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

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A001333, A000129, A048694, A048695.

Sequence in context: A270695 A048468 A255108 * A055849 A235163 A084813

Adjacent sequences: A048768 A048769 A048770 * A048772 A048773 A048774

Keyword

easy,nice,nonn

Author

Barry E. Williams

Extensions

More terms from Harvey P. Dale, May 01 2013

Status

approved