A077122 Let M_n be the n X n matrix M_(i,j) = 2^i-2^j then the characteristic polynomial of M_n = x^n-a(n)*x^(n-2).

0, 4, 56, 460, 2976, 16884, 88392, 438940, 2101232, 9794884, 44755608, 201359340, 894850368, 3937184404, 17180131304, 74446624060, 320691939984, 1374391631844, 5864066209080, 24922271951500, 105553133043680, 445668746679604, 1876499911846536

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-53,106,-96,32)

Formula

a(n) = 1/3 * [(n-2)4^(n+2) + 3*2^(n+4) - 4(n-4)]. - Ralf Stephan, May 09 2004

From Colin Barker, Aug 30 2017: (Start)

G.f.: 4*x*(1 + 2*x) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)^2).

a(n) = 12*a(n-1) - 53*a(n-2) + 106*a(n-3) - 96*a(n-4) + 32*a(n-5) for n>4.

(End)

Prog

(PARI) a(n)=polcoeff(charpoly(matrix(n, n, i, j, 2^i-2^j)), n-2)
(PARI) concat(0, Vec(4*x*(1 + 2*x) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)^2) + O(x^30))) \\ Colin Barker, Aug 30 2017

Crossrefs

Sequence in context: A255011 A201620 A204108 * A020540 A101540 A358882

Adjacent sequences: A077119 A077120 A077121 * A077123 A077124 A077125

Keyword

nonn,easy

Author

Benoit Cloitre, Nov 29 2002

Status

approved