A088981 a(n+2) = a(n+1) + a(n) - (2*n + 1) where a(0)=7, a(1)=11.

7, 11, 17, 25, 37, 55, 83, 127, 197, 309, 489, 779, 1247, 2003, 3225, 5201, 8397, 13567, 21931, 35463, 57357, 92781, 150097, 242835, 392887, 635675, 1028513, 1664137, 2692597, 4356679, 7049219, 11405839, 18454997, 29860773, 48315705, 78176411, 126492047, 204668387

Offset

0,1

References

John Baylis and Rod Haggarty, Alice in Numberland, A Student's Guide to the Enjoyment of Higher Mathematics, Macmillan Education 1988.

Geoff Buckwell, Mastering Mathematics, Palgrave Master Series, 2nd Ed. 1997.

R. P. C. Forman, Additional Mathematics Pure & Applied, Stanley Thornes, 1989.

Links

Table of n, a(n) for n=0..37.

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

Formula

a(n) = (2*alpha^(n+3) - 2*beta^(n+3) + 2*sqrt(5)*n + 3*sqrt(5)) / sqrt(5) where alpha = (1 + sqrt(5)) / 2 and beta = (1 - sqrt(5)) / 2.

From Elmo R. Oliveira, May 06 2026: (Start)

a(n) = A089061(n) + A000071(n+4).

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

G.f.: (7 - 10*x - 2*x^2 + 3*x^3)/((1 - x)^2*(1 - x - x^2)). (End)

Mathematica

LinearRecurrence[{3, -2, -1, 1}, {7, 11, 17, 25}, 40] (* Harvey P. Dale, Jun 08 2018 *)

Prog

(PARI) a=[7, 11]; for(n=2, 40, a=concat(a, a[#a]+a[#a-1]-2*n+3)); a

Crossrefs

Cf. A000071, A089061.

Sequence in context: A046132 A162337 A056687 * A257666 A224868 A021014

Adjacent sequences: A088978 A088979 A088980 * A088982 A088983 A088984

Keyword

easy,nonn

Author

Kurmang. Aziz. Rashid, Dec 01 2003

Extensions

More terms from Elmo R. Oliveira, May 06 2026

Status

approved