A279895 a(n) = n*(5*n + 11)/2.

0, 8, 21, 39, 62, 90, 123, 161, 204, 252, 305, 363, 426, 494, 567, 645, 728, 816, 909, 1007, 1110, 1218, 1331, 1449, 1572, 1700, 1833, 1971, 2114, 2262, 2415, 2573, 2736, 2904, 3077, 3255, 3438, 3626, 3819, 4017, 4220, 4428, 4641, 4859, 5082, 5310, 5543, 5781, 6024, 6272, 6525

Offset: 0

Author

Bruno Berselli, Dec 22 2016

Keywords

• nonn
• easy

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. A000566, A008589, A017281.

Second bisection of A165720.

The first differences are in A016885.

Cf. similar sequences provided by P(s,m)+s*m, where P(s,m) = ((s-2)*m^2-(s-4)*m)/2 is the m-th s-gonal number: A008585 (s=2), A055999 (s=3), A028347 (s=4), A140091 (s=5), A033537 (s=6), this sequence (s=7), A067725 (s=8).

Programs

Magma

[n*(5*n+11)/2: n in [0..60]];

Mathematica

Table[n (5 n + 11)/2, {n, 0, 60}]
LinearRecurrence[{3,-3,1},{0,8,21},60] (* Harvey P. Dale, Nov 14 2022 *)

PARI

vector(60, n, n--; n*(5*n+11)/2)

Python

[n*(5*n+11)/2 for n in range(60)]

Sage

[n*(5*n+11)/2 for n in range(60)]

Formula

O.g.f.: x*(8 - 3*x)/(1 - x)^3.

E.g.f.: x*(16 + 5*x)*exp(x)/2.

a(n+h) - a(n-h) = h*A017281(n+1), with h>=0. A particular case:

a(n) - a(-n) = 11*n = A008593(n).

a(n+h) + a(n-h) = 2*a(n) + A033429(h), with h>=0. A particular case:

a(n) + a(-n) = A033429(n).

a(n) - a(n-2) = A017281(n) for n>1. Also:

40*a(n) + 121 = A017281(n+1)^2.

a(n) = A000566(n) + 7*n, also a(n) = A000566(n) + A008589(n). - Michel Marcus, Dec 22 2016