A144448 -id:A144448 - cp's OEIS frontend

A178978 a(n) = A144448(n+1)/8.

0, 2, 5, 1, 14, 20, 1, 35, 44, 2, 65, 77, 10, 104, 119, 5, 152, 170, 7, 209, 230, 28, 275, 299, 4, 350, 377, 5, 434, 464, 55, 527, 560, 22, 629, 665, 26, 740, 779, 91, 860, 902, 35, 989, 1034, 40, 1127, 1175, 136, 1274, 1325, 17

Offset: 0

Paul Curtz, Jan 02 2011

Differs from A178971 for indices n > 23.

G. C. Greubel, Table of n, a(n) for n = 0..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).

Cf. A061039, A145910, A145911, A178971, A178977, A178978, A144448.

A061039 := proc(n) numer(1/9-1/n^2) ; end proc:
A144448 := proc(n) A061039(1+2*n) ; end proc:
A178978 := proc(n) A144448(n+1)/8 ; end proc:
seq(A178978(n),n=0..80) ; # R. J. Mathar, Jan 06 2011

Table[Numerator[1/9 -1/(2*n+3)^2]/8, {n, 0, 75}] (* G. C. Greubel, Mar 06 2022 *)

[numerator(1/9 -1/(2*n+3)^2)/8 for n in (0..75)] # G. C. Greubel, Mar 06 2022

Trisections:
  a(3*n)   = A145911(n);
  a(3*n+1) = A145910(n);
  a(3*n+2) = A178977(n).
a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81). - G. C. Greubel, Mar 06 2022

A144450 Second bisection of A061039.

Original entry on oeis.org

7, 1, 55, 91, 5, 187, 247, 35, 391, 475, 7, 667, 775, 11, 1015, 1147, 143, 1435, 1591, 65, 1927, 2107, 85, 2491, 2695, 323, 3127, 3355, 133, 3835, 4087, 161, 4615, 4891, 575, 5467, 5767, 75, 6391, 6715, 87, 7387, 7735, 899, 8455, 8827, 341, 9595, 9991, 385, 10807, 11227, 1295, 12091, 12535

Offset: 1

Paul Curtz, Oct 06 2008

nonn

Related to the Paschen spectrum of hydrogen. Contains only odd numbers. The sequence read modulo 9 is "full" and contains all numbers from 0 to 8.

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).

Cf. A061039, A144448.

Numerator[1/9 - 1/(2*Range[2, 100])^2] (* G. C. Greubel, Mar 06 2022 *)

[numerator(1/9 -1/(2*n+2)^2) for n in (1..100)] # G. C. Greubel, Mar 06 2022

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

a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81). - G. C. Greubel, Mar 06 2022

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

cp's OEIS Frontend

A178978 a(n) = A144448(n+1)/8.

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