OFFSET
0,3
COMMENTS
a(n) + a(n+1) = A001333(n+1). Inverse binomial transform of A007070 (with prepended 1). Inverse invert transform of A077995.
Floretion Algebra Multiplication Program, FAMP Code: -4ibasejseq[J*D] with J = - .25'i + .25'j + .5'k - .25i' + .25j' + .5k' - .5'kk' - .25'ik' - .25'jk' - .25'ki' - .25'kj' - .5e and D = + .5'i - .25'j + .25'k + .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,1).
FORMULA
a(n) = a(n-1) + 3*a(n-2) + a(n-3), n >= 3.
G.f.: (x-1)/((x+1)*(x^2+2*x-1)).
a(n) = (sqrt(2)/4)*((1 + sqrt(2))^n - (1 - sqrt(2))^n) + (-1)^n.
E.g.f.: cosh(x) - sinh(x) + exp(x)*sinh(sqrt(2)*x)/sqrt(2). - Stefano Spezia, May 26 2024
MATHEMATICA
LinearRecurrence[{1, 3, 1}, {1, 0, 3}, 40] (* Harvey P. Dale, Nov 24 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Aug 23 2005
STATUS
approved