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

Offset: 0

Author

Kurmang. Aziz. Rashid, Dec 01 2003

Keywords

• easy
• nonn

References

• J. Baylis and R. Haggarty, Alice in Numberland, A Student's Guide to the Enjoyment of Higher Mathematics, Macmillan Education 1988.
• G. Buckwell, Mastering Mathematics, Palgrave Master Series, 2nd Ed. 1997.
• R. P. C. Forman, Additional Mathematics Pure & Applied, Stanley Thornes, 1989.

Links

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

Programs

Mathematica

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

PARI

a=[7,11];for(n=2,10,a=concat(a,a[#a]+a[#a-1]-2*n+3)); a

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.