A152018 Denominator of 1/n^2-1/(3n)^2 or of 8/(9n^2).

9, 9, 81, 18, 225, 81, 441, 72, 729, 225, 1089, 162, 1521, 441, 2025, 288, 2601, 729, 3249, 450, 3969, 1089, 4761, 648, 5625, 1521, 6561, 882, 7569, 2025, 8649, 1152, 9801, 2601, 11025, 1458, 12321, 3249, 13689, 1800, 15129, 3969, 16641, 2178, 18225

Offset

1,1

Comments

The associated terms of the n-th main series of the Hydrogen energy spectrum are A000290(3), A061038(6), A061040(9), A061042(12), A061044(15), A061046(18), A061048(21), A061050(24), etc.

All numbers are multiples of 9.

Links

Table of n, a(n) for n=1..45.

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

Formula

Sum_{n>=1} 1/a(n) = Pi^2/27 (A291050). - Amiram Eldar, Sep 14 2022

Mathematica

Denominator/@(8/(9Range[50]^2))  (* Harvey P. Dale, Mar 15 2011 *)

Prog

(PARI) a(n)=my(q=n\4); [18*q^2, 144*q^2+72*q+9, 36*q^2+36*q+9, 144*q^2+216*q+81][n%4+1] \\ Charles R Greathouse IV, Jun 04 2026

Crossrefs

Cf. A143025 with a similar principle of construction.

Cf. A291050, A000290, A061038, A061040, A061042, A061044, A061046, A061048, A061050.

Sequence in context: A210052 A239225 A165830 * A223744 A112296 A038299

Adjacent sequences: A152015 A152016 A152017 * A152019 A152020 A152021

Keyword

nonn,easy,changed

Author

Paul Curtz, Nov 20 2008

Extensions

Stratified definition, corrected indices, extended, R. J. Mathar, Dec 10 2008

Status

approved