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

0,2

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).

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

Maple

seq(n*(7*n-3)/2, n=0..50); # G. C. Greubel, Aug 31 2019

Mathematica

Table[n*(7*n-3)/2, {n, 0, 50}] (* G. C. Greubel, Aug 23 2017 *)

Prog

(PARI) a(n)=n*(7*n-3)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n*(7*n-3)/2: n in [0..50]]; // G. C. Greubel, Aug 31 2019
(Sage) [n*(7*n-3)/2 for n in (0..50)] # G. C. Greubel, Aug 31 2019
(GAP) List([0..50], n-> n*(7*n-3)/2); # G. C. Greubel, Aug 31 2019

Crossrefs

Cf. A001106, A022264.

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

Sequence in context: A248118 A320648 A141464 * A139211 A254196 A161527

Adjacent sequences: A218468 A218469 A218470 * A218472 A218473 A218474

Keyword

nonn,easy

Author

Philippe Deléham, Mar 26 2013

Status

approved