A081034 7th binomial transform of the periodic sequence (1,8,1,1,8,1...).
1, 15, 162, 1548, 13896, 120240, 1016352, 8457408, 69618816, 568707840, 4620206592, 37384915968, 301618907136, 2428188733440, 19516934725632, 156684026953728, 1256763510521856, 10073855853527040, 80709333444329472, 646385587251314688, 5175350216190590976, 41428394838605168640
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (14,-48).
Programs
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Mathematica
RecurrenceTable[{a[0]==1,a[n]==8a[n-1]+7*6^(n-1)},a,{n,20}] (* or *) LinearRecurrence[{14,-48},{1,15},20] (* Harvey P. Dale, Jun 16 2013 *)
Formula
a(n) = 8*a(n-1) + 7*6^(n-1).
a(n) = (9/2)*8^n - (7/2)*6^n.
From Harvey P. Dale, Jun 16 2013: (Start)
a(0)=1, a(1)=15, a(n) = 14*a(n-1)-48*a(n-2).
G.f.: (x+1)/(48*x^2-14*x+1). (End)
E.g.f.: exp(6*x)*(9*exp(2*x) - 7)/2. - Stefano Spezia, Jul 23 2024