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A109803
Expansion of (x^2+1)*(x+1)^2 / ((x-1)*(x^2+x+1)*(x^2+2*x-1)).
1
1, 4, 11, 29, 72, 175, 425, 1028, 2483, 5997, 14480, 34959, 84401, 203764, 491931, 1187629, 2867192, 6922015, 16711225, 40344468, 97400163, 235144797, 567689760, 1370524319, 3308738401, 7988001124, 19284740651, 46557482429, 112399705512
OFFSET
0,2
COMMENTS
Floretion Algebra Multiplication Program, FAMP Code: 2tessumseq[C*H] with C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and H = + .5'j + .5j', sumtype: (Y[sqa.Findk()], *, sum) (internal program code)
FORMULA
a(n) = 2*a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) - a(n-5) for n>4. - Colin Barker, May 16 2019
21*a(n) = 12*( A000129(n)+4*A000129(n+1)) -4*7 +b(n) where b(n>=0) = A049347(n)+5*A049347(n-1) = 1,4,-5,1,4,-5,... periodic with period 3. - R. J. Mathar, Sep 11 2019
MATHEMATICA
LinearRecurrence[{2, 1, 1, -2, -1}, {1, 4, 11, 29, 72}, 40] (* Harvey P. Dale, May 11 2020 *)
PROG
(PARI) Vec((1 + x)^2*(1 + x^2) / ((1 - x)*(1 + x + x^2)*(1 - 2*x - x^2)) + O(x^35)) \\ Colin Barker, May 16 2019
CROSSREFS
Sequence in context: A062432 A220018 A131046 * A262280 A027968 A027970
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Aug 15 2005
STATUS
approved