A083877 Absolute value of determinant of n X n matrix where the element a(i,j) = if i + j > n then 2*(i + j -n) - 1, else 2*(n + 1 - i - j).

1, 5, 25, 101, 385, 1397, 4921, 16949, 57409, 191909, 634777, 2081477, 6775873, 21921941, 70548793, 225995285, 721032577, 2292237893, 7264134169, 22954663973, 72350776321, 227512682165, 713919106105, 2235900497141, 6990131027905, 21817681693157

Offset

1,2

Comments

The main antidiagonal is 1, the upper left elements are increasing larger even numbers and the lower right elements are increasing larger odd numbers.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-3,-9).

Formula

a(n) = 1/12 * [(4n-1)3^n - 3(-1)^n].

a(n) = 5*a(n-1)-3*a(n-2)-9*a(n-3). G.f.: x*(3*x^2+1) / ((x+1)*(3*x-1)^2). - Colin Barker, Sep 28 2014

Example

a(5) = det{ 8 6 4 2 1 / 6 4 2 1 3 / 4 2 1 3 5 / 2 1 3 5 7 / 1 3 5 7 9 } = 385.

Mathematica

f[i_, j_, n_] := Block[{a = 2*(i + j) - 2*n - 1}, If[i + j <= n, a = Abs[a - 1]]; a]; Table[ Abs[ Det[ Table[ f[i, j, n], {i, 1, n}, {j, 1, n}]]], {n, 1, 24}]
LinearRecurrence[{5, -3, -9}, {1, 5, 25}, 30] (* Harvey P. Dale, Jan 06 2017 *)

Prog

(PARI) Vec(x*(3*x^2+1)/((x+1)*(3*x-1)^2) + O(x^100)) \\ Colin Barker, Sep 28 2014
(PARI) a(n) = abs(matdet(matrix (n, n, i, j, if (i + j > n, 2*(i + j -n) - 1, 2*(n + 1 - i - j))))); \\ Michel Marcus, Sep 29 2014

Crossrefs

Sequence in context: A098111 A224415 A255459 * A293885 A209836 A272762

Adjacent sequences: A083874 A083875 A083876 * A083878 A083879 A083880

Keyword

nonn,easy

Author

Robert G. Wilson v, May 07 2003

Extensions

More terms from Colin Barker, Sep 28 2014

Definition corrected by Michel Marcus, Oct 01 2014

Status

approved