A276041 Exponential convolution of odd numbers (A005408) with themselves.

1, 6, 28, 104, 336, 992, 2752, 7296, 18688, 46592, 113664, 272384, 643072, 1499136, 3457024, 7897088, 17891328, 40239104, 89915392, 199753728, 441450496, 970981376, 2126512128, 4638900224, 10083106816, 21843935232, 47177531392, 101602820096, 218238025728

Offset

0,2

Links

Table of n, a(n) for n=0..28.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72. Erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

Index entries for linear recurrences with constant coefficients, signature (6,-12,8)

Formula

O.g.f.: (1 + 4*x^2)/(1 - 2*x)^3.

E.g.f.: (1 + 2*x)^2*exp(2*x).

a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3).

a(n) = 2^n*(n^2 + n + 1).

a(n) = A000079(n)*A002061(n+1).

Binomial transform of A053755.

Mathematica

LinearRecurrence[{6, -12, 8}, {1, 6, 28}, 29]
Table[2^n (n^2 + n + 1), {n, 0, 28}]

Crossrefs

Cf. A000079, A002061, A005408, A053755, A128796 (exponential convolution of even numbers with themselves).

Sequence in context: A172141 A172132 A011856 * A134416 A266976 A352739

Adjacent sequences: A276038 A276039 A276040 * A276042 A276043 A276044

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Aug 17 2016

Status

approved