OFFSET
1,2
COMMENTS
Primes are given in A006032.
Let A be the Hessenberg matrix of the order n, defined by: A[1,j]=1, A[i,i]:=14, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). - Milan Janjic, Feb 21 2010
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..873
Index entries for linear recurrences with constant coefficients, signature (15,-14).
FORMULA
a(n) = (14^n - 1)/13.
a(n) = 14*a(n-1) + 1 for n>1, a(1)=1. - Vincenzo Librandi, Aug 03 2010
a(n) = Sum_{i=0..n-1} 13^i*binomial(n,n-1-i). - Bruno Berselli, Nov 12 2015
From G. C. Greubel, Oct 17 2016: (Start)
G.f.: x/((1-x)*(1-14*x)).
E.g.f.: (1/13)*(exp(14*x) - exp(x)). (End)
EXAMPLE
a(4) = 2955 because (14^4-1)/13 = 38416/13 = 2955.
For n=6, a(6) = 1*6 + 13*15 + 169*20 + 2197*15 + 28561*6 + 371293*1 = 579195. - Bruno Berselli, Nov 12 2015
MATHEMATICA
Table[FromDigits[PadRight[{}, n, 1], 14], {n, 20}] (* or *) LinearRecurrence[{15, -14}, {1, 15}, 20] (* Harvey P. Dale, Aug 29 2016 *)
PROG
(Sage) [gaussian_binomial(n, 1, 14) for n in range(1, 15)] # Zerinvary Lajos, May 28 2009
(Sage) [(14^n-1)/13 for n in (1..30)] # Bruno Berselli, Nov 12 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Julien Peter Benney (jpbenney(AT)gmail.com), Feb 19 2008
STATUS
approved