A074453 Sum of determinants of 2nd order principal minors of powers of inverse of the matrix ((1,1,0,0),(1,0,1,0),(1,0,0,1),(1,0,0,0)).

6, 1, -3, 1, 17, 16, -15, -13, 81, 127, -58, -175, 329, 885, -31, -1424, 833, 5543, 2181, -9233, -2298, 31025, 27893, -49495, -54879, 150416, 245697, -204965, -526887, 570895, 1801670, -407711, -3882303, 946397, 11542929, 3442672, -24121039, -10317745, 64959629, 56727711, -127083514

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2002

Keywords

• easy
• sign

Comments

a(n) is the reflected (A074058) sequence of sequence A074193.

Links

• Index entries for linear recurrences with constant coefficients, signature (1, -2, 2, 2, 1, 1).

Crossrefs

Cf. A073817, A073937, A074058, A074081, A074193.

Programs

Mathematica

CoefficientList[Series[(6-5*x+8*x^2-6*x^3-4*x^4-x^5)/(1-x+2*x^2-2*x^3-2*x^4-x^5-x^6), {x, 0, 40}], x]
LinearRecurrence[{1,-2,2,2,1,1},{6,1,-3,1,17,16},50] (* Harvey P. Dale, Mar 16 2012 *)

Formula

a(n)=a(n-1)-2a(n-2)+2a(n-3)+2a(n-4)+a(n-5)+a(n-6).

G.f.: (6-5x+8x^2-6x^3-4x^4-x^5)/(1-x+2x^2-2x^3-2x^4-x^5-x^6).

abs(a(n)) = abs(A074193(n)). - Joerg Arndt, Oct 22 2020