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

Author

Barry E. Williams

Keywords

• easy
• nice
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A001333, A000129, A048694, A048695.

Programs

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 *)

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

Extensions

More terms from Harvey P. Dale, May 01 2013