A134965 a(1)=3, a(n) = a(n-1) + 7 + 2*mod(n-1, 2) for n>=2.

3, 12, 19, 28, 35, 44, 51, 60, 67, 76, 83, 92, 99, 108, 115, 124, 131, 140, 147, 156, 163, 172, 179, 188, 195, 204, 211, 220, 227, 236, 243, 252, 259, 268, 275, 284, 291, 300, 307, 316, 323, 332, 339, 348, 355, 364, 371, 380, 387, 396, 403, 412, 419, 428

Offset: 1

Author

Roger L. Bagula, Jan 31 2008

Keywords

• nonn
• easy

Comments

Starting weights for pyramid game.

Numbers n such that the equation m(m + 1)/2 + 1 - n == 0 mod m has a solution.

Numbers congruent to {3, 12} mod 16. - Philippe Deléham, Nov 28 2016

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Mathematica

Flatten[Table[If[ IntegerQ[2*Sqrt[ -7 + 8*n]] && Mod[n - 7, 8] == 0, f[n], {}], {n, 1, 10000}]]
LinearRecurrence[{1,1,-1},{3,12,19},60] (* Harvey P. Dale, Oct 05 2017 *)

PARI

Vec(x*(3 + 9*x + 4*x^2) / ((1 - x)^2 * (1 + x)) + O(x^100)) \\ Colin Barker, Nov 29 2016

PARI

a(n)=8*n - 4 - n%2 \\ Charles R Greathouse IV, Nov 29 2016

Formula

From R. J. Mathar, Feb 05 2008: (Start)

G.f.: (3+9*x+4*x^2)/((1-x)^2*(x+1)).

a(n) - a(n-1) = A010729(n).

(End)

From Colin Barker, Nov 29 2016: (Start)

a(n) = 8*n - 4 for n even.

a(n) = 8*n - 5 for n odd.

a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.

(End)

E.g.f.: 4 + ((16*x - 9)*exp(x) + exp(-x))/2. - David Lovler, Aug 21 2022

Extensions

Definition adapted to offset by Georg Fischer, Jun 19 2021