A090407 a(n) = Sum_{k = 0..n} C(4*n + 1, 4*k).
1, 6, 136, 2016, 32896, 523776, 8390656, 134209536, 2147516416, 34359607296, 549756338176, 8796090925056, 140737496743936, 2251799780130816, 36028797153181696, 576460751766552576, 9223372039002259456
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..800
- Index entries for linear recurrences with constant coefficients, signature (12,64).
Programs
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Mathematica
Table[Sum[Binomial[4n+1,4k],{k,0,n}],{n,0,30}] (* or *) LinearRecurrence[ {12,64},{1,6},30] (* Harvey P. Dale, Jan 19 2012 *)
Formula
From Harvey P. Dale, Jan 19 2012: (Start)
a(0) = 1, a(1) = 6, a(n) = 12*a(n-1)+64*a(n-2).
G.f.: (6*x-1)/(64*x^2+12*x-1). (End)
a(n) = (1/2) * 4^n * (4^n + (-1)^n). - Peter Bala, Feb 06 2019