A092444 a(n+1) = 11*a(n) - a(n-1) - 3, a(0)=a(1)=1.

1, 1, 7, 73, 793, 8647, 94321, 1028881, 11223367, 122428153, 1335486313, 14567921287, 158911647841, 1733460204961, 18909150606727, 206267196469033, 2250030010552633, 24544062919609927, 267734662105156561

Offset: 0

Author

N. J. A. Sloane, Sep 19 2008, based on emails from M. F. Hasler and Jim Nastos on Apr 25 2008

Keywords

• nonn

Comments

The old entry with this sequence number was a duplicate of A039963.

The simultaneous equations (p+1)(p+2) == -1 (mod q), (q+1)(q+2) == -1 (mod p), where p and q are odd, have solutions {3, 3}, {3, 21}, {7, 73}, {21, 507}, {73, 793}, {793, 8647} and suggested this recurrence.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..980
• Index entries for linear recurrences with constant coefficients, signature (12,-12,1).
• Index entries for sequences that are fixed points of mappings

Programs

Mathematica

nxt[{a_,b_}]:={b,11b-a-3}; NestList[nxt,{1,1},20][[;;,1]] (* or *) LinearRecurrence[{12,-12,1},{1,1,7},20] (* Harvey P. Dale, Jul 06 2025 *)

Formula

a(n) = 2*(A004190(n)-10*A004190(n-1))/3+1/3. G.f.: (1-11x+7x^2)/((1-x)(1-11x+x^2)). [From R. J. Mathar, Sep 20 2008]

Extensions

More terms from R. J. Mathar, Sep 20 2008