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
Keywords
Examples
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).
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).
Crossrefs
Cf. A134226.
Programs
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Magma
[1] cat [(n-1)*(n+6)/2: n in [2..70]]; // G. C. Greubel, Feb 17 2021
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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 *) -
Sage
[1]+[(n-1)*(n+6)/2 for n in (2..70)] # G. C. Greubel, Feb 17 2021
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)
Extensions
Terms a(37) onward added by G. C. Greubel, Feb 17 2021
Comments