A138238 Alternating sum of the squares of the first n Jacobsthal numbers.

0, 1, 0, 9, -16, 105, -336, 1513, -5712, 23529, -92752, 373737, -1489488, 5968873, -23853648, 95458281, -381745744, 1527157737, -6108281424, 24433824745, -97733900880, 390938399721, -1563748006480

Offset: 0

Author

Paul Barry, Mar 07 2008

Keywords

• easy
• sign

Links

• Index entries for linear recurrences with constant coefficients, signature (-2,9,2,-8).

Crossrefs

Cf. A119283.

Programs

Mathematica

LinearRecurrence[{-2,9,2,-8},{0,1,0,9},30] (* Harvey P. Dale, Feb 13 2018 *)

Formula

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

a(n)=4*2^n/9-4(-4)^n/45-(-1)^n/18-3/10;

a(n)=(13-4*J(2n+1))(-1)^n/30+4*J(n)/3-3/10, J(n)=A001045(n);

a(n)=sum{k=0..n (-1)^(k+1)*J(k)^2};