A102239 a(n) = (Sum_{i=0..n} 5^i) + 1 - (Sum_{i=0..n} 5^i) mod 2.

1, 7, 31, 157, 781, 3907, 19531, 97657, 488281, 2441407, 12207031, 61035157, 305175781, 1525878907, 7629394531, 38146972657, 190734863281, 953674316407, 4768371582031, 23841857910157, 119209289550781, 596046447753907

Offset

0,2

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1tesseq[ + 'ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj' + e]

a(n) = term (1,1) in M^n, M = the 4 X 4 matrix [1, 1, 1, 2; 1, 1, 2, 1; 1, 2, 1, 1; 2, 1, 1, 1]. a(n)/a(n-1) tends to 5, a root to the charpoly x^4 - 4x^3 - 6x^2 + 4x + 5. - Gary W. Adamson, Mar 12 2009

This is 1+A003463(n+1) rounded down to the next odd integer. - R. J. Mathar, Sep 11 2019

Links

Table of n, a(n) for n=0..21.

Robert Munafo, Sequences Related to Floretions

Index entries for linear recurrences with constant coefficients, signature (5,1,-5).

Formula

a(n) = 4*a(n-1) + 5*a(n-2) - 2 (conjecture). - Creighton Dement, Apr 13 2005

(1/4) (5^(n+1) - 2(-1)^2 + 1). - Ralf Stephan, May 17 2007

From R. J. Mathar, Mar 19 2009: (Start)

G.f.: -(-1 - 2*x + 5*x^2)/((x-1)*(5*x-1)*(1+x)).

a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3). (End)

Mathematica

a = Table[Sum[5^i, {i, 0, n}] + 1 - Mod[Sum[5^i, {i, 0, n}], 2], {n, 0, 50}]

Crossrefs

Cf. A015531.

Sequence in context: A199216 A057620 A055625 * A188233 A319457 A264608

Adjacent sequences: A102236 A102237 A102238 * A102240 A102241 A102242

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 15 2005

Status

approved