A168668 - OEIS

A168668

a(n) = n*(2 + 5*n).

0, 7, 24, 51, 88, 135, 192, 259, 336, 423, 520, 627, 744, 871, 1008, 1155, 1312, 1479, 1656, 1843, 2040, 2247, 2464, 2691, 2928, 3175, 3432, 3699, 3976, 4263, 4560, 4867, 5184, 5511, 5848, 6195, 6552, 6919, 7296, 7683, 8080, 8487, 8904, 9331, 9768, 10215, 10672

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OFFSET

0,2

COMMENTS

Appears on the main diagonal of the following table of terms of the Hydrogen series, A169603:

0, 3, 8, 15, 24, ... A005563

0, 7, 16, 1, 40, 55, ... A061039

0, 11, 24, 39, 56, 3, 96, ... A061043

0, 15, 32, 51, 72, 95, 120, ... A061047

0, 19, 40, 63, 88, 115, 144, 175, 208, 1, ...

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature(3,-3,1).

FORMULA

G.f.: x*(7 + 3*x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

First differences: a(n) - a(n-1) = 10*n-3.

Second differences: a(n) - 2*a(n-1) + a(n-2) = 10 = A010692(n).

a(n) = A131242(10n+6). - Philippe Deléham, Mar 27 2013

a(n) = A000384(n) + 6*A000217(n). - Luciano Ancora, Mar 28 2015

a(n) = A000217(n) + A000217(3*n). - Bruno Berselli, Jul 01 2016

E.g.f.: x*(7 + 5*x)*exp(x). - G. C. Greubel, Jul 29 2016

Sum_{n>=1} 1/a(n) = 5/4 - sqrt(1-2/sqrt(5))*Pi/4 + sqrt(5)*log(phi)/4 - 5*log(5)/8, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 17 2023

MAPLE

A168668:=n->n*(2+5*n): seq(A168668(n), n=0..50); # Wesley Ivan Hurt, Mar 28 2015

MATHEMATICA

f[n_]:=n*(2+5*n); f[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)

LinearRecurrence[{3, -3, 1}, {0, 7, 24}, 50] (* Harvey P. Dale, Sep 09 2021 *)

PROG

(Magma) [n*(2+5*n): n in [0..50] ]; // Vincenzo Librandi, Aug 06 2011

(PARI) vector(50, n, n--; n*(2+5*n)) \\ Derek Orr, Jun 26 2015

CROSSREFS

Cf. A000217, A000384, A001622, A010692, A131242, A254963 (comment).

Cf. A005563, A061039, A061043, A061047, A169603.

Sequence in context: A217749 A006707 A196116 * A159225 A146298 A079671