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

1,2

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)

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

Cf. A175009, A026741, A001318

Sequence in context: A213396 A011843 A080549 * A084569 A192970 A110964

Adjacent sequences: A175003 A175004 A175005 * A175007 A175008 A175009

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