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A077843
Expansion of (1-x)/(1-2*x-2*x^2-2*x^3).
1
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
OFFSET
0,3
COMMENTS
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
FORMULA
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
EXAMPLE
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,
...
- Paul Barry, Mar 01 2011
PROG
(Sage)
from sage.combinat.sloane_functions import recur_gen3
it = recur_gen3(0, 1, 1, 2, 2, 2)
[next(it) for i in range(35)] # Zerinvary Lajos, Jun 25 2008
(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 */
(PARI) Vec((1-x)/(1-2*x-2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
CROSSREFS
Sequence in context: A014143 A361476 A077994 * A061703 A126948 A131593
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved