A017313 a(n) = (10*n + 3)^9.

19683, 10604499373, 1801152661463, 46411484401953, 502592611936843, 3299763591802133, 15633814156853823, 58871586708267913, 186940255267540403, 520411082988487293, 1304773183829244583, 3004041937984268273

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Crossrefs

Cf. A001017 (n^9), A017305 (10n+3).

Programs

Magma

[(10*n+3)^9: n in [0..15]]; // Vincenzo Librandi, Jul 31 2011

Mathematica

(10*Range[0,20]+3)^9 (* or *) LinearRecurrence[ {10,-45,120,-210,252,-210,120,-45,10,-1},{19683,10604499373,1801152661463,46411484401953,502592611936843,3299763591802133,15633814156853823,58871586708267913,186940255267540403,520411082988487293},30] (* Harvey P. Dale, Sep 14 2013 *)

Python

for n in range(0, 15): print((10*n + 3)**9, end=", ") # Stefano Spezia, Oct 20 2018

Formula

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10); a(0)=19683, a(1)=10604499373, a(2)=1801152661463, a(3)=46411484401953, a(4)=502592611936843, a(5)=3299763591802133, a(6)=15633814156853823, a(7)=58871586708267913, a(8)=186940255267540403, a(9)=520411082988487293. - Harvey P. Dale, Sep 14 2013