A091775 1 + 4^n + 9^n + 16^n.
30, 354, 4890, 72354, 1108650, 17312754, 273234810, 4338079554, 69107159370, 1102999460754, 17623571298330, 281757423024354, 4506141560307690, 72080471098818354, 1153127396812683450, 18448597098193370754, 295164582378232361610, 4722516577573661689554
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (30, -273, 820, -576).
Programs
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Magma
[1+4^n+9^n+16^n : n in [1..20]]; // Wesley Ivan Hurt, Nov 26 2014
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Maple
A091775:=n->1+4^n+9^n+16^n: seq(A091775(n), n=1..20); # Wesley Ivan Hurt, Nov 26 2014
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Mathematica
Table[1 + 4^n + 9^n + 16^n, {n, 20}] (* or *) LinearRecurrence[ {30, -273, 820, -576}, {30, 354, 4890, 72354}, 20] (* Harvey P. Dale, May 04 2011 *)
Formula
For n > 0, a(n) = 5^(2*n+1)/(2*n+1)*sum(k = 0, 2*n + 1, (1/5)^k*C(2*n + 1, k)*B(k)) where B(k) is the k-th Bernoulli number.
G.f.: x*(16/(1 - 16*x) + 9/(1 - 9*x) + 4/(1 - 4*x) + 1/(1 - x)). - Harvey P. Dale, May 04 2011
a(1) = 30, a(2) = 354, a(3) = 4890, a(4) = 72354, a(n) = 30*a(n-1) - 273*a(n-2) + 820*a(n-3) - 576*a(n-4). - Harvey P. Dale, May 04 2011
Extensions
Corrected and extended by Harvey P. Dale, May 04 2011