A144448 First bisection of A061039.

0, 16, 40, 8, 112, 160, 8, 280, 352, 16, 520, 616, 80, 832, 952, 40, 1216, 1360, 56, 1672, 1840, 224, 2200, 2392, 32, 2800, 3016, 40, 3472, 3712, 440, 4216, 4480, 176, 5032, 5320, 208, 5920, 6232, 728, 6880, 7216, 280, 7912, 8272, 320, 9016, 9400, 1088, 10192, 10600, 136, 11440, 11872, 152

Offset

1,2

Comments

From Paschen spectrum of hydrogen.

All numbers are multiples of 8.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

Formula

a(n) = A061039(2*n+1).

From G. C. Greubel, Mar 06 2022: (Start)

a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81).

a(n) = 8*A178978(n). (End)

Mathematica

Table[Numerator[1/3^2 - 1/(2*n+1)^2], {n, 100}] (* G. C. Greubel, Mar 06 2022 *)

Prog

(SageMath) [numerator(1/9 -1/(2*n+1)^2) for n in (1..100)] # G. C. Greubel, Mar 06 2022
(PARI) a(n)=numerator(1/9 - 1/(2*n+1)^2) \\ Charles R Greathouse IV, May 27 2026

Crossrefs

Cf. A061039, A178978.

Sequence in context: A253152 A305362 A197603 * A070584 A205072 A185798

Adjacent sequences: A144445 A144446 A144447 * A144449 A144450 A144451

Keyword

nonn,easy

Author

Paul Curtz, Oct 06 2008

Extensions

Formula index corrected, extended by R. J. Mathar, Dec 02 2008

Status

approved