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A081034
7th binomial transform of the periodic sequence (1,8,1,1,8,1...).
4
1, 15, 162, 1548, 13896, 120240, 1016352, 8457408, 69618816, 568707840, 4620206592, 37384915968, 301618907136, 2428188733440, 19516934725632, 156684026953728, 1256763510521856, 10073855853527040, 80709333444329472, 646385587251314688, 5175350216190590976, 41428394838605168640
OFFSET
0,2
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
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 *)
CROSSREFS
Sequence in context: A323292 A067361 A014920 * A279157 A016243 A164599
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 03 2003
STATUS
approved