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A138238 Alternating sum of the squares of the first n Jacobsthal numbers. 1
0, 1, 0, 9, -16, 105, -336, 1513, -5712, 23529, -92752, 373737, -1489488, 5968873, -23853648, 95458281, -381745744, 1527157737, -6108281424, 24433824745, -97733900880, 390938399721, -1563748006480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..22.

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

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};

MATHEMATICA

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

CROSSREFS

Cf. A119283.

Sequence in context: A308248 A179307 A014720 * A177171 A226232 A267088

Adjacent sequences:  A138235 A138236 A138237 * A138239 A138240 A138241

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 07 2008

STATUS

approved

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Last modified November 29 18:31 EST 2021. Contains 349416 sequences. (Running on oeis4.)