A108924 J(n)^2+J(n+1)^2, with J(n) the Jacobsthal number A001045(n).

1, 2, 10, 34, 146, 562, 2290, 9074, 36466, 145522, 582770, 2329714, 9321586, 37280882, 149134450, 596515954, 2386107506, 9544342642, 38177545330, 152709831794, 610840026226, 2443358706802, 9773437623410, 39093744901234

Offset: 0

Author

Paul Barry, Jul 17 2005

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (3,6,-8).

Programs

Mathematica

Total/@Partition[LinearRecurrence[{1,2},{0,1},40]^2,2,1] (* or *) LinearRecurrence[ {3,6,-8},{1,2,10},40] (* Harvey P. Dale, Apr 11 2013 *)

Python

def A108924(n): return (((1<Chai Wah Wu, Apr 18 2025

Formula

G.f.: (1-x-2x^2)/((1-x)(1-4x)(1+2x)); a(n)=3a(n-1)+6a(n-2)-8a(n-3); a(n)=(5/9)4^n+(2/9)(-2)^n+2/9.

a(0)=1, a(1)=2, a(2)=10, a(n)=3*a(n-1)+6*a(n-2)-8*a(n-3). - Harvey P. Dale, Apr 11 2013