cp's OEIS Frontend

G.f.: (1 + x)^3 * (1 + x^2) * (1 - x + 2*x^2 - x^3 + 3*x^4 - x^5 + 4*x^6 - x^7 + 4*x^8 - x^9 + 4*x^10 - x^11 + 4*x^12 - x^13 + 3*x^14 - x^15 + 2*x^16 - x^17 + x^18) / ((1 - x)^3 * (1 - x + x^2 - x^3 + x^4) * (1 + x + x^2 + x^3 + x^4) * (1 + x^3 + x^6) * (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, Dec 19 2015

From N. J. A. Sloane, Feb 22 2018 (Start)

The following is a another conjectured recurrence, found by gfun, using the command rec:=gfun[listtorec](t1, a(n)); (where t1 is a list of the initial terms) suggested by Paul Zimmermann.

Note: this should not be used to extend the sequence.

0 = (-38*n^3-836*n^2-5351*n)*a(n)+(-76*n^2-798*n)*a(n+1)+(-38*n^3-912*n^2-6149*n)*a(n+2)+(-38*n^3-988*n^2-6947*n)*a(n+3)+(-38*n^3-1064*n^2-7745*n)*a(n+4)+(-38*n^3-1140*n^2 -8543*n)*a(n+5)+(-76*n^3-2052*n^2-14692*n)*a(n+6)

+ (-532*n^2-5586*n)*a(n+7)+(-76*n^3-2204*n^2-16288*n)*a(n+8)+(-684*n^2-7182*n)*a(n+9)+(-684*n^2 -7182*n)*a(n+10)+(-684*n^2-7182*n)*a(n+11)+(-684*n^2-7182*n)*a(n+12)+(76*n^3+ 988*n^2+3520*n)*a(n+13)+(-532*n^2-5586*n)*a(n+14)+(76*n^3+1140*n^2+5116*n)*a(n+15)

+ (38*n^3+456*n^2+1361*n)*a(n+16)+(38*n^3+532*n^2+2159*n)*a(n+17)+(38*n^3+608*n^2+2957*n)*a(n+18)+(38*n^3+684*n^2+3755*n)*a(n+19)+(-76*n^2-798*n)*a(n+20)+(38*n^3+760*n^2+4553*n)*a(n+21), with

a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 16, a(4) = 25, a(5) = 37, a(6) = 53, a(7) = 74, a(8) = 99, a(9) = 125, a(10) = 151, a(11) = 177, a(12) = 205, a(13) = 238, a(14) = 279, a(15) = 328, a(16) = 381, a(17) = 434, a(18) = 483, a(19) = 528, a(20) = 574, a(21) = 627

(End)