A134227 Row sums of triangle A134226.

1, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, 1269, 1320, 1372, 1425, 1479, 1534, 1590, 1647, 1705, 1764, 1824, 1885, 1947

Offset

1,2

Comments

Essentially the same as A055999. - R. J. Mathar, Mar 28 2012

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

Binomial transform of (1, 3, 2, -1, 1, -1, 1, -1, 1, ...).

From G. C. Greubel, Feb 17 2021: (Start)

a(n) = (n-1)*(n+6)/2 + [n=1].

G.f.: x*(1 +x -x^3)/(1-x)^3.

E.g.f.: 3 + x + (-6 +6*x +x^2)*exp(x)/2. (End)

Example

a(4) = 15 = sum of row 4 terms of triangle A134226: (1 + 2 + 8 + 4).
a(4) = 15 = (1, 3, 3, 1) dot (1, 3, 2, -1) = (1 + 9 + 6 - 1).

Mathematica

Table[(n-1)*(n+6)/2 + Boole[n==1], {n, 70}] (* G. C. Greubel, Feb 17 2021 *)
LinearRecurrence[{3, -3, 1}, {1, 4, 9, 15}, 70] (* Harvey P. Dale, Aug 13 2024 *)

Prog

(Sage) [1]+[(n-1)*(n+6)/2 for n in (2..70)] # G. C. Greubel, Feb 17 2021
(Magma) [1] cat [(n-1)*(n+6)/2: n in [2..70]]; // G. C. Greubel, Feb 17 2021

Crossrefs

Cf. A134226.

Sequence in context: A313299 A350547 A055999 * A022945 A022948 A022443

Adjacent sequences: A134224 A134225 A134226 * A134228 A134229 A134230

Keyword

nonn

Author

Gary W. Adamson, Oct 14 2007

Extensions

Terms a(37) onward added by G. C. Greubel, Feb 17 2021

Status

approved