A022324 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 1 and a(1) = 10.

1, 10, 12, 23, 36, 60, 97, 158, 256, 415, 672, 1088, 1761, 2850, 4612, 7463, 12076, 19540, 31617, 51158, 82776, 133935, 216712, 350648, 567361, 918010, 1485372, 2403383, 3888756, 6292140, 10180897

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Programs

Mathematica

LinearRecurrence[{2,0,-1}, {1,10,12}, 50] (* G. C. Greubel, Aug 25 2017 *)
RecurrenceTable[{a[0]==1,a[1]==10,a[n]==a[n-1]+a[n-2]+1},a,{n,30}] (* Harvey P. Dale, Nov 04 2019 *)

PARI

x='x+O('x^50); vec((1+8*x-8*x^2)/((1-x)*(1-x-x^2))) \\ G. C. Greubel, Aug 25 2017

Formula

From R. J. Mathar, Apr 07 2011: (Start)

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

a(n) = A022115(n) - 1. (End)

a(n) = 2*F(n+2) + 7*F(n) - 1, where F = A000045. - G. C. Greubel, Aug 25 2017