A024152 a(n) = 12^n - n^12.

1, 11, -3952, -529713, -16756480, -243891793, -2173796352, -13805455393, -68289495040, -277269756129, -938082635776, -2395420006033, 0, 83695120256591, 1227224552173568, 15277275236695743, 184602783918325760

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Comments

Conjecture: satisfies a linear recurrence having signature (25, -234, 1222, -4147, 9867, -17160, 22308, -21879, 16159, -8866, 3510, -949, 157, -12). - Harvey P. Dale, Jan 27 2019

The conjecture above is correct. From the general formula for {a(n)} we can see that the roots for the characteristic polynomial are one 12 and thirteen 1's, so the characteristic polynomial is (x - 12)*(x - 1)^13 = x^14 - 25*x^13 + 234*x^12 - ... + 12, with corresponding recurrence coefficients 25, -234, ..., -12. - Jianing Song, Jan 28 2019

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (25,-234,1222,-4147,9867,-17160,22308,-21879,16159,-8866,3510,-949,157,-12).

Crossrefs

Cf. A024012, A024026, A058794, A024040, A024054, A024068, A024082, A024096, A024110, A024124, A024138. - Vladimir Joseph Stephan Orlovsky, Jan 15 2009

Programs

Magma

[12^n-n^12: n in [0..20]]; // Vincenzo Librandi, Jun 30 2011

Mathematica

Table[12^n-n^12,{n,0,30}] (* Harvey P. Dale, Jan 27 2019 *)