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A111587
a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4), a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 20.
1
1, 4, 9, 20, 49, 120, 289, 696, 1681, 4060, 9801, 23660, 57121, 137904, 332929, 803760, 1940449, 4684660, 11309769, 27304196, 65918161, 159140520, 384199201, 927538920, 2239277041, 5406093004, 13051463049, 31509019100, 76069501249
OFFSET
0,2
COMMENTS
Let (b(n)) be the p-INVERT of (1,2,2,2,2,2,...) using p(S) = 1 - S^2; then
b(0) = 0 and b(n) = a(n-1) for n >= 1; see A292400. - Clark Kimberling, Sep 30 2017
Floretion Algebra Multiplication Program, FAMP Code: 2kbasekseq[J+G] with J = + j' + k' + 'ii' and G = + .5'ii' + .5'jj' + .5'kk' + .5e
FORMULA
a(2n) = A090390(n+1), a(2n+1) = A046729(n+1);
G.f.: (x+1)^2/((x^2+1)*(1-2*x-x^2)). [sign flipped by R. J. Mathar, Nov 10 2009]
a(n) = A057077(n+1)/2 - A001333(n+2)/2. - R. J. Mathar, Nov 10 2009
MATHEMATICA
LinearRecurrence[{2, 0, 2, 1}, {1, 4, 9, 20}, 30] (* Harvey P. Dale, Jul 26 2011 *)
CoefficientList[Series[(x + 1)^2 / ((x^2 + 1) (1 - 2 x - x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Oct 01 2017 *)
PROG
(Magma) I:=[1, 4, 9, 20]; [n le 4 select I[n] else 2*Self(n-1) +2*Self(n-3)+Self(n-4): n in [1..35]]; // Vincenzo Librandi, Oct 01 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Aug 08 2005
STATUS
approved