A081854 a(n) = (8*n - 3)*(4*n - 1)*(8*n^2 - 5*n + 1).

3, 60, 2093, 13398, 47415, 123728, 268065, 512298, 894443, 1458660, 2255253, 3340670, 4777503, 6634488, 8986505, 11914578, 15505875, 19853708, 25057533, 31222950, 38461703, 46891680, 56636913, 67827578, 80599995, 95096628, 111466085, 129863118, 150448623

Offset: 0

Author

N. J. A. Sloane, Apr 13 2003

Keywords

• nonn
• easy

Links

• J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Value of A081853 when started at b(0) with 2*b(0) == 5 (mod 8).

Programs

Mathematica

Table[(8n-3)(4n-1)(8n^2-5n+1),{n,0,30}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{3,60,2093,13398,47415},30] (* Harvey P. Dale, Mar 20 2015 *)

PARI

a(n)=(8*n-3)*(4*n-1)*(8*n^2-5*n+1) \\ Charles R Greathouse IV, Oct 21 2022

Formula

G.f.: (60 + 1793*x + 3533*x^2 + 755*x^3 + 3*x^4)/(1-x)^5.

a(0)=3, a(1)=60, a(2)=2093, a(3)=13398, a(4)=47415, a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, Mar 20 2015

E.g.f.: exp(x)*(3 + 57*x + 988*x^2 + 1216*x^3 + 256*x^4). - Stefano Spezia, Jun 26 2024