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A102239 a(n) = Sum[5^i, {i, 0, n}] + 1 - Mod[Sum[5^i, {i, 0, n}], 2] 0
1, 7, 31, 157, 781, 3907, 19531, 97657, 488281, 2441407, 12207031, 61035157, 305175781, 1525878907, 7629394531, 38146972657, 190734863281, 953674316407, 4768371582031, 23841857910157, 119209289550781, 596046447753907 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = term (1,1) in M^n, M = the 4x4 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. [From Gary W. Adamson, Mar 12 2009]

LINKS

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

Robert Munafo, Sequences Related to Floretions

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

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). [From R. J. Mathar, Mar 19 2009]

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A015531.

Sequence in context: A199216 A057620 A055625 * A188233 A264608 A172634

Adjacent sequences:  A102236 A102237 A102238 * A102240 A102241 A102242

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Mar 15 2005

STATUS

approved

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Last modified November 18 09:17 EST 2017. Contains 294879 sequences.