A175006 Row sums of triangle A175009.
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
Examples
a(4) = 21 = (1 + 4 + 9 + 7), where (1, 4, 9, 7) = row 4 of triangle A175009.
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1)
Programs
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PARI
Vec((1 + x^2 + 2*x^3 - x^5)/((1 - x)^5*(1 + x)^2) + O(x^50)) \\ Andrew Howroyd, Sep 01 2018
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)
Extensions
Duplicate term removed and a(15) and beyond from Andrew Howroyd, Sep 01 2018