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A099513
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Row sums of triangle A099512, so that a(n) = Sum_{k=0..n} coefficient of z^k in (1 + 3*z + z^2)^(n-[k/2]), where [k/2] is the integer floor of k/2.
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1
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1, 4, 8, 27, 89, 257, 784, 2421, 7336, 22324, 68147, 207549, 632177, 1926608, 5870089, 17884476, 54493120, 166034731, 505883825, 1541369745, 4696373312, 14309268413, 43598614528, 132839740908, 404746601923, 1233213978037
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1+2*x-x^2)/(1-2*x-x^2-7*x^3+x^4).
a(0)=1, a(1)=4, a(2)=8, a(3)=27, a(n)=2*a(n-1)+a(n-2)+7*a(n-3)- a(n-4) [From Harvey P. Dale, Jul 12 2011]
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MATHEMATICA
| LinearRecurrence[{2, 1, 7, -1}, {1, 4, 8, 27}, 30] (* or *) CoefficientList[ Series[ (1+2x-x^2)/(1-2x-x^2-7x^3+x^4), {x, 0, 30}], x] (* From Harvey P. Dale, Jul 12 2011 *)
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PROG
| (PARI) a(n)=sum(k=0, n, polcoeff((1+3*x+x^2+x*O(x^k))^(n-k\2), k))
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CROSSREFS
| Cf. A099512.
Sequence in context: A026085 A036720 A110132 * A104042 A117864 A020138
Adjacent sequences: A099510 A099511 A099512 * A099514 A099515 A099516
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 21 2004
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