OFFSET
0,2
COMMENTS
In reference to program code, 2baseiseq[X](n) = ((-1)^n)*A001353(n) (a(n)^2 + 1 is a perfect square.) 1tesseq[X](n) = (-1^(n+1))*A097948(n).
Floretion Algebra Multiplication Program, FAMP Code: 1ibaseiseq[X] with X = .5'i + .5i' + 'ii' - .5'jj' + 1.5'kk' - 1 (* Corrected by Creighton Dement, Dec 11 2009 *)
LINKS
Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (-4,0,4,1).
FORMULA
G.f.: (x^2+x+1)/((1-x)*(x+1)*(x^2+4*x+1)).
Floor(((2 + sqrt(3))^n + (2 - sqrt(3))^n)/4) produces this sequence with a different offset and without signs. - James R. Buddenhagen, May 20 2010
Define c(n) = a(n) - 4*a(n+1) - a(n+2) and d(n) = -a(n) - 4*a(n+1) - a(n+2); Conjectures: I: c(2n) = 24*A076139(n); (Triangular numbers that are one-third of another triangular number) II: c(2n+1) = -A011943(n+1); (Numbers n such that any group of n consecutive integers has integral standard deviation) III: d(2n) = -2; IV: d(2n+1) = -1
MAPLE
seriestolist(series((x^2+x+1)/((1-x)*(x+1)*(x^2+4*x+1)), x=0, 25));
MATHEMATICA
LinearRecurrence[{-4, 0, 4, 1}, {1, -3, 13, -48}, 30] (* Harvey P. Dale, Jun 15 2018 *)
PROG
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Creighton Dement, Jul 21 2005
STATUS
approved