A226451 a(n) = n*(7*n^2-12*n+7)/2.

0, 1, 11, 51, 142, 305, 561, 931, 1436, 2097, 2935, 3971, 5226, 6721, 8477, 10515, 12856, 15521, 18531, 21907, 25670, 29841, 34441, 39491, 45012, 51025, 57551, 64611, 72226, 80417, 89205, 98611, 108656, 119361, 130747, 142835, 155646, 169201, 183521

Offset: 0

Author

Bruno Berselli, Jun 07 2013

Keywords

• nonn
• easy

Comments

See the comment in A226449.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A001106.

Similar sequences of the type b(m)+m*b(m-1), where b is a polygonal number: A006003, A069778, A143690, A204674, A212133, A226449, A226450.

Programs

Magma

[n*(7*n^2-12*n+7)/2: n in [0..40]];

Magma

I:=[0,1,11,51]; [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..40]]; // Vincenzo Librandi, Aug 18 2013

Mathematica

Table[n (7 n^2 - 12 n + 7)/2, {n, 0, 40}]
CoefficientList[Series[x (1 + 7 x + 13 x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 18 2013 *)

Formula

G.f.: x*(1+7*x+13*x^2)/(1-x)^4.

a(n) = A001106(n) + n*A001106(n-1).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 4. - Wesley Ivan Hurt, Oct 15 2023