A138803 - OEIS

A138803

Imaginary parts of terms (1,1), (2,2) of matrix [1,(1+I); 1,1]^n.

0, 1, 3, 8, 20, 47, 105, 224, 456, 881, 1595, 2632, 3692, 3359, -2927, -27776, -103088, -304607, -803149, -1966392, -4549884, -10029361, -21114759, -42375200, -80491880, -142437359, -226667157, -294543992, -191015460, 556551487, 3216934945

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..31.

Index entries for linear recurrences with constant coefficients, signature (4,-4,0,-1).

FORMULA

Imaginary parts of upper left and lower right terms of matrix [1,(1+I); 1,1]^n; I^2 = -1.

a(n) = 4*a(n-1)-4*a(n-2)-a(n-4). G.f.: -x^2*(x-1) / (x^4+4*x^2-4*x+1). [Colin Barker, Dec 18 2012]

EXAMPLE

a(6) = 47 since the sixth power of the matrix generator = [(14,47); (-6,58); (26,32); (14,47)]; where (14,47) = (14 + 47*I).

CROSSREFS

Sequence in context: A026690 A036676 A101533 * A048492 A006776 A291097

Adjacent sequences: A138800 A138801 A138802 * A138804 A138805 A138806

KEYWORD

sign,easy

AUTHOR

Gary W. Adamson, Mar 30 2008

STATUS

approved