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a(n) = ((2*n+1)^5+(-1)^n)/2.
2

%I #18 Apr 04 2024 09:50:01

%S 1,121,1563,8403,29525,80525,185647,379687,709929,1238049,2042051,

%T 3218171,4882813,7174453,10255575,14314575,19567697,26260937,34671979,

%U 45112099,57928101,73504221,92264063,114672503,141237625,172512625

%N a(n) = ((2*n+1)^5+(-1)^n)/2.

%C Partial sums of A175112.

%C Convolution of the finite sequence 1,116,967,1672,967,116,1 with A001753.

%H Vincenzo Librandi, <a href="/A175111/b175111.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,5,5,-9,5,-1).

%F 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).

%F G.f: (1+116*x+967*x^2+1672*x^3+967*x^4+116*x^5+x^6)/((1+x)*(x-1)^6).

%t 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 *)

%t LinearRecurrence[{5,-9,5,5,-9,5,-1},{1,121,1563,8403,29525,80525,185647},50] (* _Harvey P. Dale_, May 30 2014 *)

%o (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

%K easy,nonn

%O 0,2

%A _R. J. Mathar_, Feb 13 2010