A218471 a(n) = n*(7*n-3)/2.
0, 2, 11, 27, 50, 80, 117, 161, 212, 270, 335, 407, 486, 572, 665, 765, 872, 986, 1107, 1235, 1370, 1512, 1661, 1817, 1980, 2150, 2327, 2511, 2702, 2900, 3105, 3317, 3536, 3762, 3995, 4235, 4482, 4736, 4997, 5265, 5540, 5822, 6111, 6407, 6710, 7020, 7337
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=7). - Bruno Berselli, Jun 10 2013
Programs
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GAP
List([0..50], n-> n*(7*n-3)/2); # G. C. Greubel, Aug 31 2019
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Magma
[n*(7*n-3)/2: n in [0..50]]; // G. C. Greubel, Aug 31 2019
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Maple
seq(n*(7*n-3)/2, n=0..50); # G. C. Greubel, Aug 31 2019
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Mathematica
Table[n*(7*n-3)/2, {n,0,50}] (* G. C. Greubel, Aug 23 2017 *) -
PARI
a(n)=n*(7*n-3)/2 \\ Charles R Greathouse IV, Jun 17 2017
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Sage
[n*(7*n-3)/2 for n in (0..50)] # G. C. Greubel, Aug 31 2019
Formula
G.f.: x*(2+5*x)/(1-x)^3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) with a(0)=0, a(1)=2, a(2)=11.
a(n) = A001106(n) + n.
a(n) = A022264(n) - n.
a(n) = A022265(n) - 2*n.
a(n) = A186029(n) - 3*n.
a(n) = A179986(n) - 4*n.
a(n) = A024966(n) - 5*n.
a(n) = A174738(7*n+1).
E.g.f.: (x/2)*(7*x + 4)*exp(x). - G. C. Greubel, Aug 23 2017