|
%I #22 Mar 26 2022 04:13:50
%S 1,3,9,18,30,45,63,84,108,135,165,198,234,273,315,360,408,459,513,570,
%T 630,693,759,828,900,975,1053,1134,1218,1305,1395,1488,1584,1683,1785,
%U 1890,1998,2109,2223,2340,2460,2583,2709,2838,2970,3105,3243,3384,3528,3675,3825
%N Row sums of triangle A134478.
%C Essentially the same as A045943. - _R. J. Mathar_, Mar 28 2012
%H G. C. Greubel, <a href="/A134479/b134479.txt">Table of n, a(n) for n = 0..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, 2, 4, -1, 1, -1, 1, ...].
%F From _Colin Barker_, Sep 24 2017: (Start)
%F G.f.: (1 + 3*x^2 - x^3) / (1 - x)^3.
%F a(n) = 3*n*(1 + n) / 2 for n>0.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End)
%e a(3) = 18 = (1, 3, 3, 1) dot (1, 2, 4, -1) = (1 + 6 + 12 -1).
%e a(3) = 18 = sum of row 3 terms of triangle A134478: (3 = 4 + 5 + 6).
%t Join[{1}, Table[Sum[n + k, {k, 0, n}], {n, 1, 50}]] (* _G. C. Greubel_, Sep 24 2017 *)
%o (PARI) concat([1], for(n=1,50, print1(sum(k=0,n, n+k), ", "))) \\ _G. C. Greubel_, Sep 24 2017
%o (PARI) Vec((1 + 3*x^2 - x^3) / (1 - x)^3 + O(x^60)) \\ _Colin Barker_, Sep 25 2017
%Y Cf. A045943, A134478.
%K nonn,easy,less
%O 0,2
%A _Gary W. Adamson_, Oct 27 2007
%E Terms a(14) onward added by _G. C. Greubel_, Sep 24 2017
|
