A144335 Row sums of triangle A144334, binomial transform of [1, 2, 6, 7, 3, 0, 0, 0, ...].

1, 3, 11, 32, 76, 156, 288, 491, 787, 1201, 1761, 2498, 3446, 4642, 6126, 7941, 10133, 12751, 15847, 19476, 23696, 28568, 34156, 40527, 47751, 55901, 65053, 75286, 86682, 99326, 113306, 128713, 145641, 164187, 184451, 206536, 230548, 256596

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (1 - 2x + 6x^2 - 3x^3 + x^4)*x/(1-x)^5.

a(n) = 1 - (5/12)*n + (3/8)*n^2 - (1/12)*n^3 + (1/8)*n^4. - R. J. Mathar, Sep 18 2008

Example

a(5) = 76 = (1, 4, 6, 4, 1) dot (1, 2, 6, 3, 7) = (1 + 8 + 36, + 28 + 3).
a(3) = 11 = sum of row 3 terms of triangle A144334: (4 + 3 + 4).

Mathematica

Table[1-5n/12+3n^2/8-n^3/12+n^4/8, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 3, 11, 32, 76}, 40] (* Harvey P. Dale, Aug 22 2016 *)

Prog

(PARI) a(n)=1-(5/12)*n+(3/8)*n^2-(1/12)*n^3+(1/8)*n^4 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Cf. A144334.

Sequence in context: A104079 A332264 A089620 * A202091 A120844 A110958

Adjacent sequences: A144332 A144333 A144334 * A144336 A144337 A144338

Keyword

nonn,easy

Author

Gary W. Adamson, Sep 18 2008

Extensions

Extended by R. J. Mathar, Sep 18 2008

Status

approved