A089061 a(0) = 5, a(1) = 7; for n>1, a(n) = a(n-1) + a(n-2) - (2*n-2).

5, 7, 10, 13, 17, 22, 29, 39, 54, 77, 113, 170, 261, 407, 642, 1021, 1633, 2622, 4221, 6807, 10990, 17757, 28705, 46418, 75077, 121447, 196474, 317869, 514289, 832102, 1346333, 2178375, 3524646, 5702957, 9227537, 14930426, 24157893, 39088247, 63246066, 102334237

Offset

0,1

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Formula

a(n) = Fibonacci(n+1) + 2*n + 4. - Ralf Stephan, Feb 24 2004

From Elmo R. Oliveira, Apr 29 2026: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4).

G.f.: (5 - 8*x - x^2 + 2*x^3)/((1 - x)^2*(1 - x - x^2)). (End)

Mathematica

RecurrenceTable[{a[0]==5, a[1]==7, a[n]==a[n-1]+a[n-2]-(2n-2)}, a, {n, 40}] (* Harvey P. Dale, Apr 23 2018 *)
(* Alternative: *)
LinearRecurrence[{3, -2, -1, 1}, {5, 7, 10, 13}, 40] (* Harvey P. Dale, Apr 23 2018 *)

Crossrefs

Cf. A000045, A088981.

Sequence in context: A287444 A196175 A112251 * A093115 A020936 A025074

Adjacent sequences: A089058 A089059 A089060 * A089062 A089063 A089064

Keyword

nonn,easy

Author

Kurmang. Aziz. Rashid, Dec 02 2003

Extensions

More terms from Elmo R. Oliveira, Apr 29 2026

Status

approved