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A048771 Partial sums of A048695. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)