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A077843
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Expansion of (1-x)/(1-2*x-2*x^2-2*x^3).
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1
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1, 1, 4, 12, 34, 100, 292, 852, 2488, 7264, 21208, 61920, 180784, 527824, 1541056, 4499328, 13136416, 38353600, 111978688, 326937408, 954539392, 2786910976, 8136775552, 23756451840, 69360276736, 202507008256, 591247473664, 1726229517312, 5039967998464
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OFFSET
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0,3
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COMMENTS
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Invert transform of the sequence 1,3,5,5,5,5,... which has g.f. (1+2x+2x^2)/(1-x). - Paul Barry, Mar 01 2011
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LINKS
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FORMULA
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a(n) = sum(k=1..n, sum(i=k..n,(sum(j=0..k, binomial(j,-3*k+2*j+i)*2^(-2*k+j+i)* binomial(k,j)))*binomial(n+k-i-1,k-1))). - Vladimir Kruchinin, May 05 2011
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EXAMPLE
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Eigensequence of the triangle
1,
3, 1,
5, 3, 1,
5, 5, 3, 1,
5, 5, 5, 3, 1,
5, 5, 5, 5, 3, 1,
5, 5, 5, 5, 5, 3, 1,
5, 5, 5, 5, 5, 5, 3, 1,
...
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PROG
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(Sage)
from sage.combinat.sloane_functions import recur_gen3
it = recur_gen3(0, 1, 1, 2, 2, 2)
(Maxima)
a(n):=sum(sum((sum(binomial(j, -3*k+2*j+i)*2^(-2*k+j+i)*binomial(k, j), j, 0, k))*binomial(n+k-i-1, k-1), i, k, n), k, 1, n); /* Vladimir Kruchinin, May 05 2011 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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