A209294 a(n) = (7*n^2 - 7*n + 4)/2.

2, 9, 23, 44, 72, 107, 149, 198, 254, 317, 387, 464, 548, 639, 737, 842, 954, 1073, 1199, 1332, 1472, 1619, 1773, 1934, 2102, 2277, 2459, 2648, 2844, 3047, 3257, 3474, 3698, 3929, 4167, 4412, 4664, 4923, 5189, 5462

Offset: 1

Author

Marco Piazzalunga, Jan 17 2013

Keywords

• nonn
• easy

Comments

a(n) is the sum of the n-th centered triangular number and n-th centered square number.

Difference of consecutive terms gives A008589 (multiples of 7).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A005448, A001844, A008589.

Programs

Magma

[(7*n^2 - 7*n + 4)/2: n in [1..30]]; // G. C. Greubel, Jan 04 2018

Mathematica

Table[(7*n^2 - 7*n + 4)/2, {n, 1, 50}] (* G. C. Greubel, Jan 04 2018 *)
LinearRecurrence[{3,-3,1},{2,9,23},40] (* Harvey P. Dale, Nov 02 2020 *)

PARI

a(n)=7*n*(n-1)/2+2 \\ Charles R Greathouse IV, Jan 17 2013

Formula

a(n) = (7*n^2 - 7*n + 4) = 7*T(n) + 2 with T = A000217.

G.f.: x*(2+3*x+2*x^2)/(1-x)^3. - Bruno Berselli, Jan 18 2013

a(n) = a(-n+1) = 3*a(n-1)-3*a(n-2)+a(n-3). - Bruno Berselli, Jan 18 2013

a(n) = 1 + A069099(n). - Omar E. Pol, Apr 27 2017

E.g.f.: ((7*x^2 + 4)*exp(x) - 4)/2. - G. C. Greubel, Jan 04 2018