A094943 -id:A094943 - cp's OEIS frontend

A109467 4 X 4 analog of A094943.

1, 26, 256, 2472, 25056, 250016, 2499456, 25002112, 249995776, 2500000256, 25000032256, 249999869952, 2500000260096, 25000000004096, 249999997894656, 2500000008404992, 24999999983190016, 250000000000065536, 2500000000134086656, 24999999999463391232

Offset: 0

N. J. A. Sloane, based on email from Alec Mihailovs, Aug 28 2005

nonn

a(n+4)=4*a(n+3)+44*a(n+2)+144*a(n+1)+160*a(n), a(0) = 1, a(1) = 26, a(2) = 256, a(3) = 2472.

G.f.: (1+22*x+108*x^2+160*x^3)/(1-4*x-44*x^2-144*x^3-160*x^4).

A094944 A sequence with a(n)/a(n-1) converging to 7, generated from a semi-magic square.

Original entry on oeis.org

1, 17, 121, 769, 5681, 39121, 274345, 1922945, 13447009, 94165777, 659108825, 4613711233, 32296542097, 226073894609, 1582520918281, 11077645104385, 77543495432897, 542804558486545, 3799631689665337, 26597422073425409

Offset: 1

Gary W. Adamson, May 25 2004

3 rows: 1 4 2, 2 1 4, 4 2 1 form a semi-magic square: row sums and columns and the diagonal = 7, the convergent of the sequence.

			a(4) = 769 since M^4 * [1 0 0] = [769 824 808].

Index entries for linear recurrences with constant coefficients, signature (3,21,49).

Cf. A094943 uses the same format and operations but with different terms.

a[n_] := (MatrixPower[{{1, 4, 2}, {2, 1, 4}, {4, 2, 1}}, n].{{1}, {0}, {0}})[[1, 1]]; Table[ a[n], {n, 10}] (* Robert G. Wilson v, May 29 2004 *)

Let M = the 3 X 3 matrix [1 4 2 / 2 1 4 / 4 2 1], then with M^n * [1 0 0] = [p q r], a(n) = p.
G.f.: -x*(7*x+1)^2 / ((7*x-1)*(7*x^2+4*x+1)). [Colin Barker, Dec 06 2012]
3*a(n) = 7^n +2 *(-1)^n *A213421(n). - R. J. Mathar, Nov 15 2019

Edited and extended by Robert G. Wilson v, May 29 2004

cp's OEIS Frontend

A109467 4 X 4 analog of A094943.

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A094944 A sequence with a(n)/a(n-1) converging to 7, generated from a semi-magic square.

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