A048772 Partial sums of A048696.

1, 10, 29, 76, 189, 462, 1121, 2712, 6553, 15826, 38213, 92260, 222741, 537750, 1298249, 3134256, 7566769, 18267802, 44102381, 106472572, 257047533, 620567646, 1498182833

Offset

0,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

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

Formula

a(n)=2*a(n-1)+a(n-2)+8; a(0)=1, a(1)=10.

a(n)=[ {(9+5*sqrt(2))(1+sqrt(2))^n - (9-5*sqrt(2))(1-sqrt(2))^n}/2*sqrt(2) ]-4.

a(0)=1, a(1)=10, a(2)=29, a(n)=3*a(n-1)-a(n-2)-a(n-3). - Harvey P. Dale, Apr 20 2012

G.f. ( 1+7*x ) / ( (x-1)*(x^2+2*x-1) ). a(n)=A048739(n)+7*A048739(n-1). - R. J. Mathar, Nov 08 2012

Mathematica

Accumulate[LinearRecurrence[{2, 1}, {1, 9}, 30]] (* or *) LinearRecurrence[ {3, -1, -1}, {1, 10, 29}, 30] (* Harvey P. Dale, Apr 20 2012 *)

Prog

(Haskell)
a048772 n = a048772_list !! n
a048772_list = scanl1 (+) a048696_list
-- Reinhard Zumkeller, Dec 15 2013
(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, -1, 3]^n*[1; 10; 29])[1, 1] \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A001333, A000129, A048694-A048696, A105082.

Sequence in context: A048469 A367343 A031129 * A055850 A200185 A321140

Adjacent sequences: A048769 A048770 A048771 * A048773 A048774 A048775

Keyword

easy,nice,nonn

Author

Barry E. Williams

Status

approved