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

Author

Reinhard Zumkeller, Apr 29 2013

Keywords

• nonn
• easy

Comments

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

a(n) = A048152(2*n-1,n), central terms;

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

a(n+1)=the remainder when n^2 is divided by 2n+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).

Programs

Haskell

a225126 n = a048152 (2 * n - 1)  n

PARI

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

Formula

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

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). - Colin Barker, May 01 2013