A056126 a(n) = n*(n + 17)/2.
0, 9, 19, 30, 42, 55, 69, 84, 100, 117, 135, 154, 174, 195, 217, 240, 264, 289, 315, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, 867, 910, 954, 999, 1045, 1092, 1140, 1189, 1239, 1290, 1342, 1395, 1449, 1504, 1560, 1617, 1675
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Programs
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GAP
List([0..50], n-> n*(n+17)/2 ); # G. C. Greubel, Jan 19 2020
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Magma
[n*(n+17)/2: n in [0..50]]; // G. C. Greubel, Jan 19 2020
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Maple
seq( n*(n+17)/2, n=0..50); # G. C. Greubel, Jan 19 2020
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Mathematica
Table[n(n+17)/2,{n,0,50}] (* Harvey P. Dale, Apr 25 2011 *) -
PARI
a(n)=n*(n+17)/2 \\ Charles R Greathouse IV, Sep 24 2015
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Sage
[n*(n+17)/2 for n in (0..50)] # G. C. Greubel, Jan 19 2020
Formula
G.f.: x*(9-8*x)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = A126890(n,8) for n>7. - Reinhard Zumkeller, Dec 30 2006
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*stirling1(n-k,i)* Product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,9), for n>=1. - Milan Janjic, Dec 20 2008
a(n) = a(n-1) + n + 8 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010
a(n) = 9*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
E.g.f.: x*(18 + x)*exp(x)/2. - G. C. Greubel, Jan 19 2020
From Amiram Eldar, Jan 10 2021: (Start)
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/17 - 1768477/20828808. (End)