A367705 Coefficients of expansion of (1 + 5*x + 11*x^2 + 5*x^3 + 7*x^4 + x^5)/(1 - x^3)^2 in powers of x.

1, 5, 11, 7, 17, 23, 13, 29, 35, 19, 41, 47, 25, 53, 59, 31, 65, 71, 37, 77, 83, 43, 89, 95, 49, 101, 107, 55, 113, 119, 61, 125, 131, 67, 137, 143, 73, 149, 155, 79, 161, 167, 85, 173, 179, 91, 185, 191, 97, 197, 203, 103, 209, 215, 109, 221, 227, 115, 233, 239

Offset

0,2

Comments

Based on an idea of Pierre CAMI.

Links

Table of n, a(n) for n=0..59.

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Formula

a(n) = 3*A006369(n) + A130196(n).

a(n) = A007310(A006369(n) + 1).

a(n) = 2*a(n-3) - a(n-6) for n >= 6.

a(3*n) = 6*n+1, a(3*n+1) = 12*n+5, a(3*n+2) = 12*n+11.

Sum_{n>=0} (-1)^n/a(n) = ((2+sqrt(2))*Pi + sqrt(3)*log(7+4*sqrt(3)) + sqrt(6)*log(5-2*sqrt(6)))/12. - Amiram Eldar, Nov 28 2023

Mathematica

CoefficientList[Series[(1 + 5*x + 11*x^2 + 5*x^3 + 7*x^4 + x^5)/(1 - x^3)^2, {x, 0, 60}], x] (* or *)
LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 5, 11, 7, 17, 23}, 60] (* Amiram Eldar, Nov 28 2023 *)

Crossrefs

Cf. A006369, A007310, A016921, A017581, A017653, A130196.

Sequence in context: A088213 A226606 A226619 * A068419 A226586 A368055

Adjacent sequences: A367702 A367703 A367704 * A367706 A367707 A367708

Keyword

nonn,easy

Author

Philippe Deléham, Nov 27 2023

Status

approved