A220083 a(n) = (15*n^2 + 9*n + 2)/2.

1, 13, 40, 82, 139, 211, 298, 400, 517, 649, 796, 958, 1135, 1327, 1534, 1756, 1993, 2245, 2512, 2794, 3091, 3403, 3730, 4072, 4429, 4801, 5188, 5590, 6007, 6439, 6886, 7348, 7825, 8317, 8824, 9346, 9883, 10435, 11002, 11584, 12181, 12793, 13420, 14062

Offset: 0

Author

Bruno Berselli, Dec 10 2012

Keywords

• nonn
• easy

Comments

Sequence related to the heptagonal numbers (A000566) by a(n) = n*A000566(n)-(n-1)*A000566(n-1).

Other similar sequences:

A005408(m) = (m+1)*A001477(m+1)-m*A001477(m), A001477 = nonn. integers;

A000326(m) = m*A000217(n)-(m-1)*A000217(m-1), A000217 = triangular numbers;

A003215(m) = (m+1)*A000290(m+1)-n*A000290(m), A000290 = square numbers;

A081267(m) = (m+1)*A000326(m+1)-n*A000326(m), A000326 = pentagonal numbers;

A080859(m) = (m+1)*A000384(m+1)-n*A000384(m), A000384 = hexagonal numbers;

A214675(m) = m*A000567(m)-(m-1)*A000567(m-1), A000567 = octagonal numbers.

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. A000326, A003215, A005408, A006597, A080859, A081267, A214675.

Programs

Magma

/* By first comment: */  A000566:=func; [n*A000566(n)-(n-1)*A000566(n-1): n in [1..45]];

Magma

[(15*n^2 + 9*n + 2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 18 2013

Maple

A220083:=n->(15*n^2 + 9*n + 2)/2; seq(A220083(n), n=0..100); # Wesley Ivan Hurt, Nov 14 2013

Mathematica

Table[(15 n^2 + 9 n + 2)/2, {n, 0, 45}]
CoefficientList[Series[(1 + 10 x + 4 x^2) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2013 *)

Maxima

A220083(n):=(15*n^2 + 9*n + 2)/2$ makelist(A220083(n),n,0,20); /* Martin Ettl, Dec 11 2012 */

PARI

a(n)=(15*n^2+9*n+2)/2 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (1+10*x+4*x^2)/(1-x)^3.

Sum( a(i), i=0..n ) = A006597(n+1).

a(n) + a(-n) = A010005(n) for n>0.