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

%I #14 Jun 08 2024 00:00:58

%S 7,11,17,25,37,55,83,127,197,309,489,779,1247,2003,3225,5201,8397,

%T 13567,21931,35463,57357,92781,150097,242835,392887,635675,1028513,

%U 1664137,2692597,4356679,7049219,11405839,18454997

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

%D J. Baylis and R. Haggarty, Alice in Numberland, A Student's Guide to the Enjoyment of Higher Mathematics, Macmillan Education 1988.

%D G. Buckwell, Mastering Mathematics, Palgrave Master Series, 2nd Ed. 1997.

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

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).

%F 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.

%t LinearRecurrence[{3,-2,-1,1},{7,11,17,25},40] (* _Harvey P. Dale_, Jun 08 2018 *)

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

%K easy,nonn

%O 0,1

%A _Kurmang. Aziz. Rashid_, Dec 01 2003