A202141 a(n) = 13*n^2 - 16*n + 5.

5, 2, 25, 74, 149, 250, 377, 530, 709, 914, 1145, 1402, 1685, 1994, 2329, 2690, 3077, 3490, 3929, 4394, 4885, 5402, 5945, 6514, 7109, 7730, 8377, 9050, 9749, 10474, 11225, 12002, 12805, 13634, 14489, 15370, 16277, 17210, 18169, 19154, 20165, 21202, 22265

Offset: 0

Author

Bruno Berselli, Dec 12 2011

Keywords

• nonn
• easy
• changed

Comments

Numbers of the form (r*n - r + 1)^2 + ((r+1)*n - r)^2; in this case, r=2.

Inverse binomial transform of this sequence: 5,-3, 26, 0, 0 (0 continued).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A190816 (r=1), A154355 (r=3), A161587.

Programs

Magma

[13*n^2-16*n+5: n in [0..42]];

Maple

A202141:=n->13*n^2-16*n+5: seq(A202141(n), n=0..100); # Wesley Ivan Hurt, Oct 09 2017

Mathematica

Table[13 n^2 - 16 n + 5, {n, 0, 42}]
LinearRecurrence[{3,-3,1},{5,2,25},50] (* Harvey P. Dale, Aug 23 2025 *)

PARI

for(n=0, 42, print1(13*n^2-16*n+5", "));

Formula

G.f.: (5 - 13*x + 34*x^2)/(1-x)^3.

a(n) = A161587(n-1) + 1 with A161587(-1) = 4.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. - Wesley Ivan Hurt, Oct 09 2017

E.g.f.: (5 - 3*x + 13*x^2)*exp(x). - Elmo R. Oliveira, Oct 20 2024