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URL: https://oeis.org/A092444

⇱ A092444 - OEIS

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A092444
a(n+1) = 11*a(n) - a(n-1) - 3, a(0)=a(1)=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.
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]
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 *)
CROSSREFS
Sequence in context: A121127 A376435 A071060 * A099141 A084768 A357165
KEYWORD
nonn
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