A362179 Main diagonal of the square array A058395.

1, 1, 4, 10, 25, 61, 146, 344, 800, 1840, 4192, 9472, 21248, 47360, 104960, 231424, 507904, 1110016, 2416640, 5242880, 11337728, 24444928, 52559872, 112721920, 241172480, 514850816, 1096810496, 2332033024, 4949278720, 10485760000, 22179479552, 46841987072

Offset

0,3

Comments

Binomial transform of 1, 0, 3, 0, 6, 0, 10, 0, 15, 0, ... (triangular numbers alternating with zeros).

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 5.

a(n) = A158920(n+1) - A158920(n).

a(n) = Sum_{k=0..n} A007318(n,k)*A008805(k)*(1 + (-1)^k)/2.

G.f.: (1-x)^5/(1-2*x)^3.

From Enrique Navarrete, Dec 18 2025: (Start)

a(n) = 2^(n-6)*(n^2 + 13*n + 32), n >= 3.

a(n+1) = 1 + Sum_{k=0..n} A291013(k).

E.g.f: (1/16)*(exp(2*x)*(x^2 + 7*x + 8) + x^2 - 7*x + 8). (End)

Mathematica

LinearRecurrence[{6, -12, 8}, {1, 1, 4, 10, 25, 61}, 50] (* Paolo Xausa, Jan 22 2026 *)

Crossrefs

Cf. A000217, A007318, A008805, A058395, A158920.

Cf. A291013.

Sequence in context: A276599 A281867 A298806 * A033539 A020748 A021004

Adjacent sequences: A362176 A362177 A362178 * A362180 A362181 A362182

Keyword

nonn,easy

Author

Philippe Deléham, Apr 10 2023

Status

approved