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

1,1

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).

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

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 *)

Prog

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

Crossrefs

Sequence in context: A273701 A273709 A139273 * A273419 A273447 A273406

Adjacent sequences: A185936 A185937 A185938 * A185940 A185941 A185942

Keyword

nonn,easy

Author

Amir H. Farrahi, Feb 06 2011

Status

approved