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A134227 Row sums of triangle A134226. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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.

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 *)

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: A313298 A313299 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

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)