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A111352
a(n+3) = a(n+2) + 3*a(n+1) + a(n).
1
1, -1, 2, 0, 5, 7, 22, 48, 121, 287, 698, 1680, 4061, 9799, 23662, 57120, 137905, 332927, 803762, 1940448, 4684661, 11309767, 27304198, 65918160, 159140521, 384199199, 927538922, 2239277040, 5406093005
OFFSET
0,3
COMMENTS
a(n) + a(n+1) = A000129(n); a(n+2) - a(n) = A001333(n)
Floretion Algebra Multiplication Program, FAMP Code: 2jbasekrokseq[A*H] with A = + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e; H = - 2'i - 'j + 'k; roktype : Y[15] = Y[15] + (-1)^p (internal program code)
FORMULA
a(n) = (1/4*sqrt(2)-1/4)*(1+sqrt(2))^n + (-1/4*sqrt(2)-1/4)*(1-sqrt(2))^n + 3/2*(-1)^n.
G.f.: (2*x-1)/((x+1)*(x^2+2*x-1)).
a(n) = 3*(-1)^n/2+A001333(n-1)/2, n>0. [R. J. Mathar, Nov 10 2009]
MATHEMATICA
LinearRecurrence[{1, 3, 1}, {1, -1, 2}, 30] (* Harvey P. Dale, Jul 26 2020 *)
CROSSREFS
Sequence in context: A084258 A171016 A321205 * A173343 A334059 A133446
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Oct 29 2005
STATUS
approved