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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; internal format)
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OFFSET
| 0,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-1).
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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)/(1-3*x+x^2+x^3). - Paul D. Hanna (pauldhanna(AT)juno.com), 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 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 16 2008]
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MATHEMATICA
| t={1, 5}; Do[AppendTo[t, t[[-2]] + 2*t[[-1]] + 3], {n, 40}]; t (* From Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)
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PROG
| (PARI) a(n)=polcoeff((1+2*x)/(1-3*x+x^2+x^3)+x*O(x^n), n) (Hanna)
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CROSSREFS
| Cf. A005409, A098790.
Sequence in context: A187198 A097507 A052951 * A127980 A054486 A072130
Adjacent sequences: A048742 A048743 A048744 * A048746 A048747 A048748
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams
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