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

0,3

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

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)). - R. J. Mathar, Sep 20 2008

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 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -12, 12]^n*[1; 1; 7])[1, 1] \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A004190, A039963.

Sequence in context: A121127 A376435 A071060 * A099141 A084768 A357165

Adjacent sequences: A092441 A092442 A092443 * A092445 A092446 A092447

Keyword

nonn,easy,changed

Author

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

Extensions

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

Status

approved