A226450 a(n) = n*(3*n^2 - 5*n + 3).

0, 1, 10, 45, 124, 265, 486, 805, 1240, 1809, 2530, 3421, 4500, 5785, 7294, 9045, 11056, 13345, 15930, 18829, 22060, 25641, 29590, 33925, 38664, 43825, 49426, 55485, 62020, 69049, 76590, 84661, 93280, 102465, 112234, 122605, 133596, 145225, 157510, 170469

Offset: 0

Author

Bruno Berselli, Jun 07 2013

Keywords

• nonn
• easy

Comments

See the comment in A226449.

For n >= 3, also the detour index of the n-barbell graph. - Eric W. Weisstein, Dec 20 2017

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Barbell Graph
• Eric Weisstein's World of Mathematics, Detour Index
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000567.

Similar sequences of the type b(m)+m*b(m-1), where b is a polygonal number: A006003, A069778, A143690, A204674, A212133, A226449, A226451.

Programs

Magma

[n*(3*n^2-5*n+3): n in [0..40]];

Magma

I:=[0,1,10,45]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // Vincenzo Librandi, Aug 18 2013

Mathematica

Table[n (3 n^2 - 5 n + 3), {n, 0, 40}]
CoefficientList[Series[x (1 + 6 x + 11 x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 10, 45, 124}, {0, 20}] (* Eric W. Weisstein, Dec 20 2017 *)

PARI

a(n) = n*(3*n^2 - 5*n + 3); \\ Altug Alkan, Dec 20 2017

Formula

G.f.: x*(1+6*x+11*x^2)/(1-x)^4.

a(n) = A000567(n) + n*A000567(n-1).