A255413 a(n) = 15*n - 11 + (n mod 2). Row 3 of Ludic array A255127.

5, 19, 35, 49, 65, 79, 95, 109, 125, 139, 155, 169, 185, 199, 215, 229, 245, 259, 275, 289, 305, 319, 335, 349, 365, 379, 395, 409, 425, 439, 455, 469, 485, 499, 515, 529, 545, 559, 575, 589, 605, 619, 635, 649, 665, 679, 695, 709, 725, 739, 755, 769, 785, 799, 815, 829, 845, 859, 875, 889, 905, 919, 935, 949, 965, 979, 995, 1009

Offset: 1

Author

Antti Karttunen, Feb 22 2015

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Row 3 of A255127.

Cf. A007310, A016921, A084967, A255407.

Programs

Mathematica

a[n_] := 15 n + Mod[n, 2] - 11;
Array[a, 100] (* Jean-François Alcover, Mar 14 2016 *)

PARI

apply( {A255413(n)=15*n-11+n%2}, [1..50]) \\ M. F. Hasler, Nov 09 2024

Scheme

;; two alternatives:
(define (A255413 n) (A255127bi 3 n)) ;; Code for A255127bi given in A255127.
(define (A255413 n) (A007310 (- (* 5 n) 3)))

Formula

a(n) = A007310((5*n)-3).

a(n) = A255407(A084967(n)) = A255407(5*A007310(n)).

a(2n+1) = 5*A016921(n) for all n >= 0.

From M. F. Hasler, Nov 09 2024: (Start)

a(n) = a(n-1) + a(n-2) + a(n-3) for n > 3, a(1..3) = (5, 19, 35).

a(n) = a(n-2) + 30 for n > 2, with a(1..2) = (5, 19).

a(2n-1) = 30n - 25, a(2n) = 30n - 11.

G.f.: x*(5 + 14*x + 11*x^2)/((1 - x)^2*(1 + x)). (End)

E.g.f.: 11 + (15*x - 11)*cosh(x) + 5*(3*x - 2)*sinh(x). - Stefano Spezia, Nov 12 2024

Extensions

New definition from M. F. Hasler, Nov 09 2024