A096881 Expansion of g.f. (1 + 4*x)/(1 - 17*x^2).
1, 4, 17, 68, 289, 1156, 4913, 19652, 83521, 334084, 1419857, 5679428, 24137569, 96550276, 410338673, 1641354692, 6975757441, 27903029764, 118587876497, 474351505988, 2015993900449, 8063975601796, 34271896307633, 137087585230532, 582622237229761, 2330488948919044
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,17).
Programs
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Magma
I:=[1,4,17]; [n le 3 select I[n] else 17*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 26 2016
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Mathematica
CoefficientList[Series[(1+4x)/(1-17x^2),{x,0,30}],x] (* or *) LinearRecurrence[ {0,17},{1,4},30] (* Harvey P. Dale, Jan 21 2012 *) -
PARI
Vec((1+4*x)/(1-17*x^2) + O(x^40)) \\ Michel Marcus, Jan 26 2016
Formula
a(n) = 3*a(n-1) + 4*a(n-2) + 17^floor((n-2)/2).
a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2), k)*4^(n-2*k).
a(n) = 17*a(n-2), n>1. - Harvey P. Dale, Jan 21 2012
E.g.f.: cosh(sqrt(17)*x) + 4*sinh(sqrt(17)*x)/sqrt(17). - Stefano Spezia, Mar 31 2023
Extensions
More terms from Stefano Spezia, Mar 31 2023