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

Author

Philippe Deléham, Apr 10 2023

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

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

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.