A158186 a(n) = 10*n^2 - 7*n + 1.

1, 4, 27, 70, 133, 216, 319, 442, 585, 748, 931, 1134, 1357, 1600, 1863, 2146, 2449, 2772, 3115, 3478, 3861, 4264, 4687, 5130, 5593, 6076, 6579, 7102, 7645, 8208, 8791, 9394, 10017, 10660, 11323, 12006, 12709, 13432, 14175, 14938, 15721, 16524, 17347

Offset

0,2

Comments

Sequence found by reading the segment (1, 4) together with the line (one of the diagonal axes) from 4, in the direction 4, 27, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 10 2011

Links

Table of n, a(n) for n=0..42.

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

Formula

a(n) = (2*n-1)*(5*n-1).

a(n) = A033571(n) - A008596(n) = A010010(n) - A033571(n).

G.f.: (1+x+18*x^2)/(1-x)^3. - Jaume Oliver Lafont, Mar 27 2009

a(n) = a(n-1) + 20*n - 17 (with a(0)=1). - Vincenzo Librandi, Dec 03 2010

Sum_{n>=0} 1/a(n) = 1 + (2*sqrt(1+2/sqrt(5))*Pi - 2*sqrt(5)*log(phi) - 5*log(5) + 8*log(2))/12, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 22 2022

Mathematica

Table[10n^2-7n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 4, 27}, 50] (* Harvey P. Dale, Apr 06 2020 *)

Prog

(PARI) a(n)=10*n^2-7*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A001622, A008596, A010010, A033571, A085787.

Sequence in context: A227866 A356814 A180576 * A272858 A272818 A356433

Adjacent sequences: A158183 A158184 A158185 * A158187 A158188 A158189

Keyword

nonn,easy

Author

Reinhard Zumkeller, Mar 13 2009

Extensions

Typo in definition corrected by Reinhard Zumkeller, Dec 03 2009

Status

approved