A226449 a(n) = n*(5*n^2-8*n+5)/2.

0, 1, 9, 39, 106, 225, 411, 679, 1044, 1521, 2125, 2871, 3774, 4849, 6111, 7575, 9256, 11169, 13329, 15751, 18450, 21441, 24739, 28359, 32316, 36625, 41301, 46359, 51814, 57681, 63975, 70711, 77904, 85569, 93721, 102375, 111546, 121249, 131499, 142311, 153700

Offset

0,3

Comments

Sequences of the type b(m)+m*b(m-1), where b is a polygonal number:

A006003(n) = A000217(n) + n*A000217(n-1) (b = triangular numbers);

A069778(n) = A000290(n+1) + (n+1)*A000290(n) (b = square numbers);

A143690(n) = A000326(n+1) + (n+1)*A000326(n) (b = pentagonal numbers);

A212133(n) = A000384(n) + n*A000384(n-1) (b = hexagonal numbers);

a(n) = A000566(n) + n*A000566(n-1) (b = heptagonal numbers);

A226450(n) = A000567(n) + n*A000567(n-1) (b = octagonal numbers);

A226451(n) = A001106(n) + n*A001106(n-1) (b = nonagonal numbers);

A204674(n) = A001107(n+1) + (n+1)*A001107(n) (b = decagonal numbers).

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).

Formula

G.f.: x*(1+5*x+9*x^2)/(1-x)^4.

a(n) - a(-n) = A008531(n) for n>0.

Mathematica

Table[n (5 n^2 - 8 n + 5)/2, {n, 0, 40}]
CoefficientList[Series[x (1 + 5 x + 9 x^2)/(1 - x)^4, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 9, 39}, 50] (* Harvey P. Dale, May 19 2017 *)

Prog

(Magma) [n*(5*n^2-8*n+5)/2: n in [0..40]];
(Magma) I:=[0, 1, 9, 39]; [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
(PARI) a(n)=n*(5*n^2-8*n+5)/2 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. (see the comment) A000566, A006003, A069778, A143690, A204674, A212133, A226450, A226451.

Sequence in context: A192608 A158447 A281381 * A299280 A023163 A054121

Adjacent sequences: A226446 A226447 A226448 * A226450 A226451 A226452

Keyword

nonn,easy

Author

Bruno Berselli, Jun 07 2013

Status

approved