A017638 a(n) = (12n+9)^10.

3486784401, 16679880978201, 1531578985264449, 34050628916015625, 362033331456891249, 2446194060654759801, 12157665459056928801, 48398230717929318249, 162889462677744140625, 480682838924478847449

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

From Fermat's little theorem, it follows that all terms are congruent to 1 mod 11 except when n is congruent to 2 mod 11 (because for those n, 12*n+9 is a multiple of 11). - Alonso del Arte, Dec 02 2013

Links

• Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

Crossrefs

Cf. A011557, A017629.

Programs

Magma

[(12*n+9)^10 : n in [0..20]]; // Wesley Ivan Hurt, Nov 25 2021

Maple

A017638:=n->(12*n+9)^10; seq(A017638(n), n=0..20); # Wesley Ivan Hurt, Dec 02 2013

Mathematica

Table[(12n + 9)^10, {n, 0, 20}] (* Wesley Ivan Hurt, Dec 02 2013 *)

Formula

a(n) = (12*n+9)^10.

a(n) = A011557(A017629(n)). - Wesley Ivan Hurt, Dec 02 2013

a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11). - Wesley Ivan Hurt, Nov 25 2021