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

Author

Reinhard Zumkeller, Mar 13 2009

Keywords

• nonn
• easy

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

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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

Extensions

Typo in definition corrected by Reinhard Zumkeller, Dec 03 2009