A275016 a(n) = (2^n - (-1+i)^n - (-1-i)^n)/4 - 1 where i is the imaginary unit.

0, 0, 0, 5, 5, 15, 35, 55, 135, 255, 495, 1055, 2015, 4095, 8255, 16255, 32895, 65535, 130815, 262655, 523775, 1048575, 2098175, 4192255, 8390655, 16777215, 33550335, 67117055, 134209535, 268435455, 536887295, 1073709055, 2147516415, 4294967295, 8589869055, 17180000255

Offset

1,4

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Omran Ahmadi, Robert Granger, An efficient deterministic test for Kloosterman sum zeros, arXiv:1104.3882 [math.NT], 2011-2012. See 4th column of Table 1 p. 9.

Robert Granger, On the Enumeration of Irreducible Polynomials over GF(q) with Prescribed Coefficients, arXiv:1610.06878 [math.AG], 2016. See 4th column of Table 1 p. 13.

Index entries for linear recurrences with constant coefficients, signature (1,2,2,-4).

Formula

G.f.: 5*x^4/((1 - x)*(1 - 2*x)*(1 + 2*x + 2*x^2)). - Ilya Gutkovskiy, Nov 12 2016

a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) - 4*a(n-4) for n>4. - Colin Barker, Nov 12 2016

a(n) = - 2^(n-2)*a(4-n) for all n in Z. - Michael Somos, Nov 13 2016

Example

G.f. = 5*x^4 + 5*x^5 + 15*x^6 + 35*x^7 + 55*x^8 + 135*x^9 + 255*x^10 + ...

Prog

(PARI) a(n) = (2^n - (-1+I)^n - (-1-I)^n)/4 -1;
(PARI) concat(vector(3), Vec(5*x^4/((1-x)*(1-2*x)*(1+2*x+2*x^2)) + O(x^50))) \\ Colin Barker, Nov 14 2016

Crossrefs

Sequence in context: A302511 A178821 A145599 * A189316 A370236 A356049

Adjacent sequences: A275013 A275014 A275015 * A275017 A275018 A275019

Keyword

nonn,easy

Author

Michel Marcus, Nov 12 2016

Status

approved