A330357 a(n) = (2*n^2 + 9 - (-1)^n)/4.

2, 3, 4, 7, 10, 15, 20, 27, 34, 43, 52, 63, 74, 87, 100, 115, 130, 147, 164, 183, 202, 223, 244, 267, 290, 315, 340, 367, 394, 423, 452, 483, 514, 547, 580, 615, 650, 687, 724, 763, 802, 843, 884, 927, 970, 1015, 1060, 1107, 1154, 1203, 1252, 1303, 1354, 1407

Offset

0,1

Links

Table of n, a(n) for n=0..53.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

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

a(n) = a(-n) for all n in Z. a(n) = A105343(n) if n>=1.

Example

G.f. = 2 + 3*x + 4*x^2 + 7*x^3 + 10*x^4 + 15*x^5 + 20*x^6 + 27*x^7 + ...

Mathematica

Table[(2 n^2+9-(-1)^n)/4, {n, 0, 60}] (* or *) LinearRecurrence[{2, 0, -2, 1}, {2, 3, 4, 7}, 60] (* Harvey P. Dale, Apr 19 2023 *)

Prog

(PARI) {a(n) = (2*n^2 + 9 - (-1)^n)/4};

Crossrefs

Cf. A105343, A267459.

Sequence in context: A160644 A347734 A267459 * A145467 A325341 A039841

Adjacent sequences: A330354 A330355 A330356 * A330358 A330359 A330360

Keyword

nonn,easy

Author

Michael Somos, Dec 11 2019

Extensions

Previous Mathematica program adjusted by Harvey P. Dale, Apr 19 2023

Status

approved