A128183 Row sums of triangle A128182.

1, 2, 7, 20, 54, 140, 352, 864, 2080, 4928, 11520, 26624, 60928, 138240, 311296, 696320, 1548288, 3424256, 7536640, 16515072, 36044800, 78381056, 169869312, 367001600, 790626304, 1698693120, 3640655872, 7784628224, 16609443840, 35366371328, 75161927680

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Formula

From Andrew Howroyd, Sep 21 2025: (Start)

a(n) = Sum_{k=0..n} binomial(n,k)*floor(k/2+1)^2.

G.f.: (1 - 4*x + 7*x^2 - 6*x^3 + 2*x^4)/(1 - 2*x)^3. (End)

Example

a(3) = 20 = sum of row 3 terms of A128182: (2 + 6 + 8 + 4).

Prog

(PARI) Vec((1 - 4*x + 7*x^2 - 6*x^3 + 2*x^4)/(1 - 2*x)^3 + O(x^31)) \\ Andrew Howroyd, Sep 21 2025

Crossrefs

Cf. A008794, A128182.

Sequence in context: A050532 A050513 A348571 * A027418 A035508 A018033

Adjacent sequences: A128180 A128181 A128182 * A128184 A128185 A128186

Keyword

nonn,easy

Author

Gary W. Adamson, Feb 17 2007

Extensions

Offset corrected and a(10) onwards from Andrew Howroyd, Sep 21 2025

Status

approved