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A175006
Row sums of triangle A175009.
2
1, 3, 9, 21, 44, 81, 139, 222, 339, 495, 701, 963, 1294, 1701, 2199, 2796, 3509, 4347, 5329, 6465, 7776, 9273, 10979, 12906, 15079, 17511, 20229, 23247, 26594, 30285, 34351, 38808, 43689, 49011, 54809, 61101, 67924, 75297, 83259, 91830, 101051, 110943, 121549, 132891
OFFSET
1,2
FORMULA
From Andrew Howroyd, Sep 01 2018: (Start)
a(n) = n + Sum{k=1..n} (n-k+1)*(binomial(k+1, 2) - binomial(floor(k/2)+1, 2) - 1).
a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7) for n > 7.
G.f.: x*(1 + x^2 + 2*x^3 - x^5)/((1 - x)^5*(1 + x)^2).
(End)
EXAMPLE
a(4) = 21 = (1 + 4 + 9 + 7), where (1, 4, 9, 7) = row 4 of triangle A175009.
PROG
(PARI) Vec((1 + x^2 + 2*x^3 - x^5)/((1 - x)^5*(1 + x)^2) + O(x^50)) \\ Andrew Howroyd, Sep 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 03 2010
EXTENSIONS
Duplicate term removed and a(15) and beyond from Andrew Howroyd, Sep 01 2018
STATUS
approved