A175111 a(n) = ((2*n+1)^5+(-1)^n)/2.
1, 121, 1563, 8403, 29525, 80525, 185647, 379687, 709929, 1238049, 2042051, 3218171, 4882813, 7174453, 10255575, 14314575, 19567697, 26260937, 34671979, 45112099, 57928101, 73504221, 92264063, 114672503, 141237625, 172512625
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).
Programs
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Magma
I:=[1, 121, 1563, 8403, 29525, 80525, 185647]; [n le 7 select I[n] else 5*Self(n-1) - 9*Self(n-2) + 5*Self(n-3) + 5*Self(n-4) - 9*Self(n-5) + 5*Self(n-6) - Self(n-7): n in [1..40]]; // Vincenzo Librandi, Dec 19 2012
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Mathematica
CoefficientList[Series[(1 + 116*x + 967*x^2 + 1672*x^3 + 967*x^4 + 116*x^5 + x^6)/((1 + x)*(x - 1)^6), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *) LinearRecurrence[{5,-9,5,5,-9,5,-1},{1,121,1563,8403,29525,80525,185647},50] (* Harvey P. Dale, May 30 2014 *)
Formula
a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7).
G.f: (1+116*x+967*x^2+1672*x^3+967*x^4+116*x^5+x^6)/((1+x)*(x-1)^6).
Comments