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A048745 Partial sums of A048654. 2
1, 5, 14, 36, 89, 217, 526, 1272, 3073, 7421, 17918, 43260, 104441, 252145, 608734, 1469616, 3547969, 8565557, 20679086, 49923732, 120526553, 290976841, 702480238, 1695937320, 4094354881, 9884647085, 23863649054, 57611945196, 139087539449, 335787024097 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..29.

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

FORMULA

a(n)=2*a(n-1)+a(n-2)+3; a(0)=1, a(1)=5.

a(n)=[ {(4+(5/2)*sqrt(2))(1+sqrt(2))^n - (4-(5/2)*sqrt(2))(1-sqrt(2))^n}/ 2*sqrt(2) ]-3/2.

G.f.: (1+2*x)/((x-1)*(x^2+2*x-1)). - Paul D. Hanna, Feb 22 2005

a(n)=3*a(n-1)-a(n-2)-a(n-3), n>2 ; a(0)=1, a(1)=5, a(2)=14. - Philippe Deléham, Dec 16 2008

2*a(n) = A135532(n+2)-3. - R. J. Mathar, Mar 06 2013

MATHEMATICA

t={1, 5}; Do[AppendTo[t, t[[-2]] + 2*t[[-1]] + 3], {n, 40}]; t (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)

PROG

(PARI) a(n)=polcoeff((1+2*x)/(1-3*x+x^2+x^3)+x*O(x^n), n) \\ Paul D. Hanna

CROSSREFS

Cf. A005409, A098790.

Sequence in context: A187198 A097507 A052951 * A307462 A292170 A224716

Adjacent sequences:  A048742 A048743 A048744 * A048746 A048747 A048748

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

STATUS

approved

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)