A225126 Central terms of the triangle in A048152.

0, 1, 4, 2, 7, 3, 10, 4, 13, 5, 16, 6, 19, 7, 22, 8, 25, 9, 28, 10, 31, 11, 34, 12, 37, 13, 40, 14, 43, 15, 46, 16, 49, 17, 52, 18, 55, 19, 58, 20, 61, 21, 64, 22, 67, 23, 70, 24, 73, 25, 76, 26, 79, 27, 82, 28, 85, 29, 88, 30, 91, 31, 94, 32, 97, 33, 100

Offset

1,3

Comments

a(n+1) = the remainder when n^2 is divided by 2*n+1. - J. M. Bergot, Jun 25 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

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

Formula

a(1) = 0, a(2*n) = n and a(2*n+1) = 3*n+1.

a(n) = A123684(n) for n > 1.

a(n) = A048152(2*n-1,n).

a(n) = A060036(2*n-1,n-1) for n > 1.

From Colin Barker, May 01 2013: (Start)

a(n) = 2*a(n-2)-a(n-4) for n>5.

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

Mathematica

LinearRecurrence[{0, 2, 0, -1}, {0, 1, 4, 2, 7}, 100] (* Paolo Xausa, Mar 10 2026 *)

Prog

(Haskell)
a225126 n = a048152 (2 * n - 1)  n
(PARI) a(n)=n--^2%(2*n+1) \\ Charles R Greathouse IV, Jun 25 2013

Crossrefs

Cf. A048152, A060036, A123684.

Sequence in context: A026189 A026213 A319556 * A123684 A180076 A169756

Adjacent sequences: A225123 A225124 A225125 * A225127 A225128 A225129

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 29 2013

Status

approved