A214525 a(n) = 7*a(n-1) - 23*a(n-2) + 49*a(n-3) - 49*a(n-4) with a(0)=0, a(1)=1, a(2)=7, a(3)=19.

0, 1, 7, 19, 21, 4, 133, 937, 2667, 3439, 2128, 20569, 132867, 392743, 596869, 647596, 3539109, 19881229, 60254719, 106198903, 158297664, 643809889, 3117087967, 9564827611, 19050869061, 34555674196, 119658973525, 507648339217, 1561117435059, 3421971910543

Offset: 0

Author

N. J. A. Sloane, Aug 07 2012, based on a posting to the Sequence Fans Mailing List by R. K. Guy, Jul 29 2009

Keywords

• nonn
• easy

Comments

This is a divisibility sequence.

It factors over the Eisenstein-Jacobi integers into two 2nd order sequences (with w^3 = 1): 0, 1, w+3, 3w+5, 4w+5, 2, -12w-1, -29w+3, ... and its conjugate (replace w by w^2). The relation for this is a(n) = (w+3)a(n-1) - (2w+3)a(n-2).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• R. K. Guy, New sequence?, SeqFan, 2009
• Hugh Williams and R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory, 7(5) (2011), 1255-1277.
• Index entries for linear recurrences with constant coefficients, signature (7,-23,49,-49).

Programs

Mathematica

RecurrenceTable[{a[0] == 0, a[1] == 1, a[2] == 7, a[3] == 19, a[n] == 7 a[n - 1] - 23 a[n - 2] + 49 a[n - 3] - 49 a[n - 4]}, a[n], {n, 0, 29}] (* Bruno Berselli, Aug 08 2012 *)
LinearRecurrence[{7,-23,49,-49},{0,1,7,19},30] (* Harvey P. Dale, Jan 02 2023 *)

Formula

G.f.: x*(1-7*x^2) /(1-7*x+23*x^2-49*x^3+49*x^4). - Bruno Berselli, Aug 08 2012

Extensions

a(9) corrected by Bruno Berselli, Aug 08 2012