A016838 -id:A016838 - cp's OEIS frontend

A017630 a(n) = (12*n+9)^2.

81, 441, 1089, 2025, 3249, 4761, 6561, 8649, 11025, 13689, 16641, 19881, 23409, 27225, 31329, 35721, 40401, 45369, 50625, 56169, 62001, 68121, 74529, 81225, 88209, 95481, 103041, 110889, 119025, 127449, 136161, 145161, 154449, 164025, 173889, 184041, 194481

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A016838.

Subsequence of A000290.

(12*Range[0,40]+9)^2 (* or *) LinearRecurrence[{3,-3,1},{81,441,1089},40] (* Harvey P. Dale, Mar 31 2012 *)

a(n)=(12*n+9)^2 \\ Charles R Greathouse IV, Jun 17 2017

From Harvey P. Dale, Mar 31 2012: (Start)
a(0)=81, a(1)=441, a(2)=1089, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).
G.f.: -9*(x^2+22*x+9)/(x-1)^3. (End)
a(n) = 9*A016838(n). - R. J. Mathar, Mar 21 2016

More terms from Jason Yuen, Sep 01 2025

A174679 a(4n) = n^2. a(4n+1) = (4n-1)^2. a(4n+2) = (2n)^2. a(4n+3) = (4n+1)^2.

Original entry on oeis.org

0, 1, 0, 1, 1, 9, 4, 25, 4, 49, 16, 81, 9, 121, 36, 169, 16, 225, 64, 289, 25, 361, 100, 441, 36, 529, 144, 625, 49, 729, 196, 841, 64, 961, 256, 1089, 81, 1225, 324, 1369, 100, 1521, 400, 1681, 121, 1849, 484, 2025, 144, 2209, 576

Offset: 0

Paul Curtz, Nov 30 2010

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

LinearRecurrence[{0,0,0,3,0,0,0,-3,0,0,0,1},{0,1,0,1,1,9,4,25,4,49,16,81},80] (* Harvey P. Dale, Apr 01 2018 *)

a(2n) = A174595(n).
a(2n+1) = A016754(n-1) = (2n-1)^2, n>0.
a(4n+1) = A016838(n-1).
a(4n+2) = A016742(n).
a(4n+3) = A016814(n).
a(n)= +3*a(n-4) -3*a(n-8) +a(n-12).
G.f.: -x*(1+x^2+x^3+6*x^4+4*x^5+22*x^6+x^7+25*x^8+4*x^9+9*x^10) / ( (x-1)^3*(1+x)^3*(x^2+1)^3 ). - R. J. Mathar, Dec 01 2010
a(n) = ((16-(1+(-1)^n)*(5+i^n))*n-4*(8-(1+(-1)^n)*(3+i^n)))^2/256, where i=sqrt(-1). - Bruno Berselli, Jan 27 2011 - Apr 09 2011

cp's OEIS Frontend

A017630 a(n) = (12*n+9)^2.

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