|
%I #11 Jul 03 2023 08:45:07
%S 1,4,9,15,22,30,39,49,60,72,85,99,114,130,147,165,184,204,225,247,270,
%T 294,319,345,372,400,429,459,490,522,555,589,624,660,697,735,774,814,
%U 855,897,940,984,1029,1075,1122,1170,1219,1269,1320,1372,1425,1479,1534,1590,1647,1705,1764,1824,1885,1947
%N Row sums of triangle A134226.
%C Essentially the same as A055999. - _R. J. Mathar_, Mar 28 2012
%H G. C. Greubel, <a href="/A134227/b134227.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F Binomial transform of (1, 3, 2, -1, 1, -1, 1, -1, 1, ...).
%F From _G. C. Greubel_, Feb 17 2021: (Start)
%F a(n) = (n-1)*(n+6)/2 + [n=1].
%F G.f.: x*(1 +x -x^3)/(1-x)^3.
%F E.g.f.: 3 + x + (-6 +6*x +x^2)*exp(x)/2.
%e a(4) = 15 = sum of row 4 terms of triangle A134226: (1 + 2 + 8 + 4).
%e a(4) = 15 = (1, 3, 3, 1) dot (1, 3, 2, -1) = (1 + 9 + 6 - 1).
%t Table[(n-1)*(n+6)/2 + Boole[n==1], {n, 70}] (* _G. C. Greubel_, Feb 17 2021 *)
%o (Sage) [1]+[(n-1)*(n+6)/2 for n in (2..70)] # _G. C. Greubel_, Feb 17 2021
%o (Magma) [1] cat [(n-1)*(n+6)/2: n in [2..70]]; // _G. C. Greubel_, Feb 17 2021
%Y Cf. A134226.
%K nonn
%O 1,2
%A _Gary W. Adamson_, Oct 14 2007
%E Terms a(37) onward added by _G. C. Greubel_, Feb 17 2021
|
