A235332 a(n) = n*(9*n + 25)/2 + 6.

6, 23, 49, 84, 128, 181, 243, 314, 394, 483, 581, 688, 804, 929, 1063, 1206, 1358, 1519, 1689, 1868, 2056, 2253, 2459, 2674, 2898, 3131, 3373, 3624, 3884, 4153, 4431, 4718, 5014, 5319, 5633, 5956, 6288, 6629, 6979, 7338, 7706, 8083, 8469, 8864, 9268, 9681, 10103

Offset: 0

Author

Bruno Berselli, Jan 22 2014

Keywords

• nonn
• easy

Comments

This is the case d=6 of n*(9*n + 4*d + 1)/2 + d. Other similar sequences are:

d=0, A022267;

d=1, A064225;

d=2, A062123;

d=3, A064226;

d=4, A022266 (with initial 0);

d=5, A178977.

First bisection of A235537.

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. A017257 (first differences), A022266, A022267, A062123, A064225, A064226, A081267, A178977, A235537.

Programs

Magma

[n*(9*n+25)/2+6: n in [0..50]];

Mathematica

Table[n (9 n + 25)/2 + 6, {n, 0, 50}]
LinearRecurrence[{3,-3,1},{6,23,49},50] (* Harvey P. Dale, Feb 12 2022 *)

PARI

a(n)=n*(9*n+25)/2+6 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (6 + 5*x - 2*x^2)/(1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

2*a(n) - a(n+1) + 12 = A081267(n).

E.g.f.: exp(x)*(12 + 34*x + 9*x^2)/2. - Elmo R. Oliveira, Nov 13 2024