A185939 a(n) = 9*n^2 - 6*n + 2.

5, 26, 65, 122, 197, 290, 401, 530, 677, 842, 1025, 1226, 1445, 1682, 1937, 2210, 2501, 2810, 3137, 3482, 3845, 4226, 4625, 5042, 5477, 5930, 6401, 6890, 7397, 7922, 8465, 9026, 9605, 10202, 10817, 11450

Offset: 1

Author

Amir H. Farrahi, Feb 06 2011

Keywords

• nonn
• easy

Comments

Group the set of natural numbers in set of 3 (1, 2, 3; 4, 5, 6; 7, 8, 9; ...) In each group, multiply the first two numbers and then add the third number to the result to get the corresponding entry in our sequence.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Mathematica

CoefficientList[Series[-x*(x + 5)*(2*x + 1)/(x - 1)^3, {x,0,50}], x] (* or *) LinearRecurrence[{3, -3, 1}, {5, 26, 65}, 50] (* G. C. Greubel, Feb 25 2017 *)
Table[9n^2-6n+2,{n,40}] (* or *) #[[1]]#[[2]]+#[[3]]&/@Partition[Range[111],3]  (* Harvey P. Dale, Apr 08 2022 *)

PARI

x='x+O('x^50); Vec(-x*(x+5)*(2*x+1)/(x-1)^3) \\ G. C. Greubel, Feb 25 2017

Formula

G.f. -x*(x+5)*(2*x+1) / (x-1)^3 . - Alexander R. Povolotsky, Feb 06 2011

a(n) = a(n-1) + 18*n - 15, a(1) = 5. - Vincenzo Librandi, Feb 07 2011

a(n) = (2*n-1)^2 + (2*n)^2 + (n-1)^2. - Bruno Berselli, Feb 06 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - G. C. Greubel, Feb 25 2017

E.g.f.: (9*x^2 + 3*x + 2)*exp(x) - 2. - G. C. Greubel, Jul 23 2017